My units in a year >>>
More seriously, I think this is a sensible way to approach it.
You definitely could take the approach of making units insanely smart. You are correct, however, that it would require major rebalances and I think that it may not even quite be the same game it is today - it is a very definite and different direction. You are also correct about the tradeoff of speeding up projectile speeds or making units less responsive.
I like the approach of slowly improving dodging over time. I think there is a pareto principle at work here - fixing the major stuff will be more significant than fixing.
I also wonder whether there are ways to do it other than tracking projectiles. Proximity to certain units, for example could trigger dodging behaviour for certain units - for example if an impaler and maybe other artillery units are spotted this might trigger dodging behaviour - as could taking damage.