I'm a veteran 4e player and DM and have a few thoughts.
On improv using the 4e framework - Great! That's the stuff of great games. 4e does a great job of supporting this for DMs by providing a nice chart of recommended DCs and damage expressions by level. I do a lot of on the fly adjudication of player stunts in my games and encourage my players to use their abilities creatively outside of combat.
On combat grind and player resiliency - Pre-MM3 monsters had defenses too high and damage too low. To compensate, I now use the 13th Age Escalation Die mechanic in my 4e games, and boost pre-MM3 monster damage. +5 damage per tier per attack is a good rule of thumb. For example, a level 12 monster should get +10 damage to any attack or ability which deals damage to the PCs. I also try to avoid using abilities that stun or take away player turns. If even that damage isn't enough to drop at least one PC per combat below zero, then up it by another +5. Every group is different. I have two leaders in my group, and they are pretty resilient so I hammer them with tough encounters.
Now, as far as combat taking too long, I don't mean to sound rude, but this is entirely on the group. Not the game. Every PC's entire turn can be taken in 30 seconds or less. Every player should know what their PC can do since 4e makes it easy by laying it all out on their sheet. Every player should spend the turns they aren't actively doing something by paying attention in battle and reviewing their abilities. When their turn comes up, it should be Standard this, Move here, Minor that, Done! In fact, for simpler classes, like the Essentials classes, even 30 seconds is more than needed. I played a Slayer once and was done with my turn in 10 seconds or less most of the time. Literally 10 seconds.
We had a real problem with long combats and found it was due to analysis paralysis and too many players not paying attention and not knowing their PCs. Well, these things build on each other and pretty soon every turn takes 10 minutes because no one is paying attention and has to be brought up to speed and then looks over their sheet, etc. As DM, you need to put a halt to this behavior. I expect all my players to know their PCs abilities intimately. Especially the casual ones. Then I time them. Any actions not started within 30 seconds are lost. Skipped. Too bad. Next player up.
You'll find that 30 seconds is a long time. As turns speed up, players won't have as much time to get distracted by other things. They'll find they need to pay attention to be ready to go. It might take a session or two, but then your game will be humming along. Also, its important that as DM, you are ready to go with your monsters, since once your players speed up, you will be the time bottleneck. As DM, I try to take each monsters turn within one minute. Before any encounter, I pause the game for a quick break to review all the monsters in the upcoming battle, so I'm not the one wasting everyone's time trying to decide what to do once the battle starts. There are tricks to this but its too much to explain now.
Another thing I recommend is to designate one player to manage the initiative for the combat. Usually, the player most likely to disengage, or get off topic, is the best choice. Have them track everyone's initiative, even the monsters, and call out the players who are up and then let the next player in line know they are up next. You can also designate them, or another player, as timekeeper whose job is to keep everyone within the 30 second limit (except for the DM). This actively engages that player, and is one less thing you have to deal with as DM.