I understand the difficulties of developing AI, especially in one where reflexes aren't important. There are some areas where it could easily be improved though, such as taking a city which it can't hold because the unit will die next turn. Spotting that is a case of brute force calculation rather than elegant routines.
AIs will never keep up with players though, not until learning routines become practical, which is why I suggest a moddable AI, probably through some scripting system. Without a moddable AI, your every day AI starts out okay, then falls behind the more strategies the developer never anticipated come out, or as ones the AI uses are dismissed as weak. A developer can't anticipate everything, and non-moddable AIs suffer heavily because of it.
For your arguments regarding 2v2, it's obviously a matter of opinion, but I'd point to Battle of Wesnoth to show that not only do people not mind the downtime, but team games are often by far and away the most popular mode of play. I just had a 1v1 where I was hoping for MORE down time as I was stumbling in my chat typing
As for the UI, I'd say it's on the generous side as is and could easily be shrunk. For example, there's no need for an entire pane dedicated to displaying target details, this pane could easily come and go as required.
However, I understand your limits, but I also know that without feedback there's no way of knowing what players think and want... so here's mine