I have suffered through the same issues you have had, and at my table I've deduced the two main problems. First, my table has usually had 7 PCs, of which anywhere from 2 to 4 of them have healing capability (or even worse, a Moon Druid)-- and this has boosted the number of potential HP at the table for the PCs through the roof. And second, none of the standard monsters in standard enemy party composition do nearly enough damage via their regular statblocks to make themselves a challenge. I either have to use the extremely esoteric and high CR monsters repeatedly (which for me is horrible for the stories my groups usually go on), or I have to throw double the amounts of monsters on the table. And doing THAT is what causes the extended time for battles when we have 7 PCs (plus any/all companions or spell items) versus 12 to 15 monsters on the table.
Other people will tell you "What do you mean? Our combat so super-quick!" and while they are not wrong, I'm pretty sure the stories of their tables are not matching up to what either you or I are experiencing.
Size of the party matters.
The types of monsters you throw at them matters.
The number of monsters you throw at them matters.
The number of healers and healing magic available matters.
The synergy (or lack thereof) of the classes in the party matters.
The focus and attention of the players to the fight at the table matters.
The skill of the players in performing tactical combat maneuvers quickly matters.
The capability of optimizing PCs for combat matters.
The narration the DM and the players give to their actions in combat matters.
Etc. etc. etc.
Any and all of these things can make combat go fast as all get out, as well as slow down to a crawl. I know in my campaigns that just ended with 7 PCs (plus companions, familiars, and hangers-on) all in the 7-9th level range (averaging like 45 to 80 HP or so), I was having to basically assign Max damage of the various monster statblocks to even begin to put dents in the PCs, or reskin massive CR monsters for use as high-level humanoid enemies. It was a pain in the rear. Extremely. So I get you.
Which brings me to my main point-- I think what you are doing is great, and I hope it works out for you. And on a similar note of your changes, I've begun working on my own new hack that I'm thinking about using for my next campaign to see if I can change up the manner of combat too.
Biggest thing I'm looking at? PCs will start the campaign with their HP set at 3rd level (IE Max HD+CON mod, half HD+CON mod, half HD+CON mod) and then it never goes up.
That's right. PCs will always only have 3rd level hit points the entire game. They will have to change their focus on what getting into combat actually means. It won't be the "standard" method for dealing with problems-- "Let's just run in there and KILL THEM ALL!". No, that's a good way to really get the party killed.
But what I like about it is that it keeps the numbers manageable. If you only have like 20 HP normally... spells that give you Temp HP or bonus HP are actually meaningful. Spells or features that raise you Armor Class are more meaningful because not getting hit is much more important than trying to just out-damage the monsters. I mean isn't that one of the biggest "truisms" players say of the game? "The best defense is a good offense! Throwing all resources at blitzing the monsters down to 0 HP as quickly as possible is the safest way to play!" Well, that doesn't work out as well if a monster party can take a PC out in a single round if they get lucky on initiative and where that PC finds themself.
On top of this is another advantage/change I would like to have in my toolbox, which is being able to use low CR humanoids creatures through the entirety of the campaign because they make sense for the stories (without needing to constantly jury-rig new statblocks to make things like lizardmen an actual potential threat even when the PCs are "6th level" or "8th level" or whatever.) I would love it if being a dual-wielder PC was an worthwhile tactical choice because it was physically possible to actually down two monsters in a single round once with each weapon... because using kobolds six months into the campaign was actually still viable. Or all those "take a free attack on a second target after downing the first" being actually useful and cool and potentially fatal on that second monster, rather than just a couple dinky plinks on the 150+ HP of the second creature.
Massive HP levels on both sides I find to just be... less... compelling? There is something I (and I think my players) find a little disheartening when a PC manages an attack that does like 75 HP of damage... only to get told "Well, that doesn't even drop the monster to half hit points yet". Huge attacks seem virtually meaningless because I have to throw gigantic sacks of HP onto the table just so they can survive long enough to even attempt an attack against the PCs or two.
So lowering the amount of HP on the table across the board is the one remaining bastion of sanity I have left to make combats past like session 6 maintain a sense of narrative and tactical sense. You seem to have the same idea, so I'm interested to see what yours results in. I have absolutely no idea how keeping all PCs at 3rd level hit points for the entirety of the new campaign will work. Maybe it does cause problems later on, or maybe it does hamstring some of the potential bigger monsters I could use down the line... but I've had the alternative, and I just don't want it anymore.
Best of luck!
Other people will tell you "What do you mean? Our combat so super-quick!" and while they are not wrong, I'm pretty sure the stories of their tables are not matching up to what either you or I are experiencing.
Size of the party matters.
The types of monsters you throw at them matters.
The number of monsters you throw at them matters.
The number of healers and healing magic available matters.
The synergy (or lack thereof) of the classes in the party matters.
The focus and attention of the players to the fight at the table matters.
The skill of the players in performing tactical combat maneuvers quickly matters.
The capability of optimizing PCs for combat matters.
The narration the DM and the players give to their actions in combat matters.
Etc. etc. etc.
Any and all of these things can make combat go fast as all get out, as well as slow down to a crawl. I know in my campaigns that just ended with 7 PCs (plus companions, familiars, and hangers-on) all in the 7-9th level range (averaging like 45 to 80 HP or so), I was having to basically assign Max damage of the various monster statblocks to even begin to put dents in the PCs, or reskin massive CR monsters for use as high-level humanoid enemies. It was a pain in the rear. Extremely. So I get you.
Which brings me to my main point-- I think what you are doing is great, and I hope it works out for you. And on a similar note of your changes, I've begun working on my own new hack that I'm thinking about using for my next campaign to see if I can change up the manner of combat too.
Biggest thing I'm looking at? PCs will start the campaign with their HP set at 3rd level (IE Max HD+CON mod, half HD+CON mod, half HD+CON mod) and then it never goes up.
That's right. PCs will always only have 3rd level hit points the entire game. They will have to change their focus on what getting into combat actually means. It won't be the "standard" method for dealing with problems-- "Let's just run in there and KILL THEM ALL!". No, that's a good way to really get the party killed.
But what I like about it is that it keeps the numbers manageable. If you only have like 20 HP normally... spells that give you Temp HP or bonus HP are actually meaningful. Spells or features that raise you Armor Class are more meaningful because not getting hit is much more important than trying to just out-damage the monsters. I mean isn't that one of the biggest "truisms" players say of the game? "The best defense is a good offense! Throwing all resources at blitzing the monsters down to 0 HP as quickly as possible is the safest way to play!" Well, that doesn't work out as well if a monster party can take a PC out in a single round if they get lucky on initiative and where that PC finds themself.
On top of this is another advantage/change I would like to have in my toolbox, which is being able to use low CR humanoids creatures through the entirety of the campaign because they make sense for the stories (without needing to constantly jury-rig new statblocks to make things like lizardmen an actual potential threat even when the PCs are "6th level" or "8th level" or whatever.) I would love it if being a dual-wielder PC was an worthwhile tactical choice because it was physically possible to actually down two monsters in a single round once with each weapon... because using kobolds six months into the campaign was actually still viable. Or all those "take a free attack on a second target after downing the first" being actually useful and cool and potentially fatal on that second monster, rather than just a couple dinky plinks on the 150+ HP of the second creature.
Massive HP levels on both sides I find to just be... less... compelling? There is something I (and I think my players) find a little disheartening when a PC manages an attack that does like 75 HP of damage... only to get told "Well, that doesn't even drop the monster to half hit points yet". Huge attacks seem virtually meaningless because I have to throw gigantic sacks of HP onto the table just so they can survive long enough to even attempt an attack against the PCs or two.
So lowering the amount of HP on the table across the board is the one remaining bastion of sanity I have left to make combats past like session 6 maintain a sense of narrative and tactical sense. You seem to have the same idea, so I'm interested to see what yours results in. I have absolutely no idea how keeping all PCs at 3rd level hit points for the entirety of the new campaign will work. Maybe it does cause problems later on, or maybe it does hamstring some of the potential bigger monsters I could use down the line... but I've had the alternative, and I just don't want it anymore.
Best of luck!