Interesting...
I'm not sure I agree with everything you've written, but I think you are on the right track. I'd say your number 1 is the most important, followed closely by 2 and 3.
In my game we keep the multiple to-hit rolls, we just roll them all at the same time.
And rather than ditch the damage die we do what the book says and roll one damage die and apply it to all hits.
But we roll the damage die with the to-hit die, which speeds things up more than you'd think.
For my take on it check out the
Combat Notes page on my campaign portal.
As I've mentioned elsewhere we also use reward tokens to encourage players to finish their turn in under 2 minutes. You can see all the details at the
Rewards page on my campaign portal. But basically the reward is a +1 chip they can apply to any roll and which they can upgrade to +2 or +3. The +3 is also an "upgrade any configrmed hit to a critical". This speeds up combat in a number of ways. Besides positively reinforcing players who play smoothly and quickly it increases the number of hits and the party damage output. Especially when the players get the hang of using them.
Finally I'd point out that it isn't really
all the player's fault (although I understand you aren't really serious about that). The DM does have his part to play in the area of grind. I'd encourage any DM to read
Stalker0’s Guide to Anti-grind and at least try what he explains, it really does make a difference.