Very very interesting topic. I try to put some input:
1. About a minimal modification of FIDE chess for lowering the 1st-move ad.
If promotion is so much important factor in causing the 1st-move ad, we can
just weaken the promotion, i.e. promoting the pawn to a ferz.
2. What do you think about the 1st-move ad of Balanced Marseillais chess?
3. I think it is quite safe to say that, in general, with the increasing
complexity (size of the game tree) of a chess variant we have a decreasing
the 1st-move ad, due to the “noise†factor. In that respect I expect
the 1st-move ad is much low in Chief than in FIDE chess.
4. I read in Arimaa the 1st-move ad is considered null (even if it is a
race game). What do you think about that? Maybe not null but very very
small… The reason maybe is because the very high complexity of the game.
(Or maybe it relevant the shortrange nature of the pieces too.)
5. About detecting the strength of the 1st-move ad in Chief. You can play Chief with the first player passing the first 5 (or more) turns.