Fairer versions of chess varients

One common theme of popular chess varients is that they often have a large first-move advantage for white.

These are just brainstorms of modifications to these varients which would reduce the first-move advantage (but hopefully not enough that there's a large advantage for black instead).

Fischer Random/960: Not really needed to be honest, according to engines most positions are more balanced than standard chess. But tournaments commonly remove the most unbalanced postions, you can do that.

Horde: Has already been balanced to make it more fair, compared to the original concept. Could be a model for other varients.

Duck: To start with, there is no duck. Black places the duck for the first time in any of the first four moves, and both sides use the duck from then on.

Crazyhouse: To start with, there is no drop rule. Black can drop pieces/pawns for the first time in the four moves after their first capture, and both sides can drop pieces from then on.

Atomic: Swap one of Black's minor pieces for an extra rook.

3-Check: White's first check does not count if black can make a check before they can make a second one.

Giveaway/Antichess: I can't really get my head around this varient, but apparently there is a forced win for white somewhere. Make whatever change you need to disrupt this forced win.

Would these work? Do you have any of your own ideas?

I can only comment on 3-Check - White does seem to get a significant plus with 1.e4 (or maybe 1.Nc3).
However, a good solution is to play 3-Check 960, which to me is more interesting anyway. I played some correspondence games of this, also did some experiments with engines, and in most cases White's advantage was significantly reduced. Plus people don't automatically know the best way to start, which may further reduce any White advantage.