The timer in battle is a minor issue.

What's needed is simultaneous turns, the elimination of restarts (especially restarts due to encounters), as short a time control as possible, and contact maps that are played for no more than 3 weeks (with an average of 2 weeks).

The goal is to have a complete game take no more than 4 hours, so that a guaranteed game can be played in an evening.

Simultaneous turns and contact maps are mutually exclusive game modes. The only type of map that allows for contact play from the very beginning and partially solves the problem of the first-move advantage is mirrored maps with several small starting positions.
And that's where the timer plays a crucial role. On average, it may not significantly reduce the time (due to the size of the map itself, the time is small), but in some cases, it will eliminate excessive delays.