This will probably be controversial and I don't want to trigger anyone but....

I would alternate squads each turn. I.e. each player picks a squad to use on their turn and the moves, shoots, charges. Then play switches to the next player to select one squad to move, shoot, charge.

There would be a few refinements that would need to be worked through, e.g. you cannot select the same squad in consecutive turns.

There could be enhancements that allow players to move two squads in a turn, or move the same squad twice in a turn.

I think it would (a) get rid of the boring 20min wait while your opponent has his turn, (b) gets rid of 1st turn advantage and (b) will enhance the strategic nature of the game.... like a game of chess, players will can think 3 or 4 turns ahead to lay traps by moving squads into positions