I was just about to make pretty much the same post (@OP), but since you beat me too it, I don't have to bother. I agree with most of the things you're saying though. Not getting rid of parties, though.
One thing that you didn't mention that I think could make a big positive impact is in movement. Right now, the game seems to be based around a movement of 1 or 2. This should be at least doubled. Standard movement should be 5 squares, with cavalry getting 8-10 and things like catapults getting only 2 or 3. This can open up a lot of tactical depth in combat. If you also go a step forward and add positioning bonuses (more damage if attacking from the side/behind) then there's even more to it.
That, along with changing the way the grids are (I agree exactly with the OP, the grid should be smaller with larger units taking up more squares), could help make tactical combat a lot more interesting than the fairly monotonous affair it is today. It could also make it feel like it's going faster, even if it's all balanced out so it's actually taking the same amount of time.
With these two changes, you start having situations where frontage matters. That big dragon is powerful, but it also takes up a lot of space, so you can both have more people attacking at the same time, and it can have a harder time maneuvering to get in a good striking range of important enemy units.
I realize that changing the way the grid works could be expensive from a dev standpoint, but I think it's important to salvage tactical combat. It does seem on the level of a feature that could show up in that free expansion, though...