I would suggest this:
Firstly, I think that the fights should be able to be seen real time, maybe not exactly real time, but have it spit out one thing, wait, then spit out the next. Watch-ability would add a LOT to this game.
Then, after that is set up, I think that the feature to slighty tune strategies in between rounds should be implemented. Like, give 3-5 choices of what to, ie. multiple choice:
A. Keep strategy
B. Increase ______ (pick 1 from list)
C. Decrease ______ (pick 1 from list)
D. All Out
E. Conserve All
etc...
I think that if you did both of those, it would be much harder on Mr. Tycoon to implement, but I think that it would be much more rewarding. Even making it so that the first round would go, then give each manager 1 minute to check the fight, and change strategy, and if they do not log in at that time and change it, then the rounds will continue as usual.
Just some ideas..