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Which antichess variant is the most balanced?

With antichess being recently solved as a forced win as white, my major gripe with the game has been that even under best play, black still plays at a severe, unholdable disadvantage the entire game, since white's initiative is far too rewarding to be neutralized with best play.

I've recently been doing research into alternate variants of antichess, and I'm curious as to the community's thoughts on if any of these proposed rule changes could result in a more balanced game where black at least has some way to draw:

1. Pawns must always promote to queens; stalemates end in a draw.

In this variant, white's initiative isn't as powerful because if they don't manage to completely eliminate all their pieces in one chain reaction, black can easily force stalemate. Even worse, the side with the least activity can be forced to promote to a queen, which is almost a guarantee that they will lose. Black is significantly stronger in this variant.

2. Kings can castle, but being checkmated results in a loss. If all other pieces except the king are captured, it's a win.

Much like the first variant, this variant discourages sweeps that fail to win every piece. If white leaves themselves with only a king and pawn, then achieving checkmate/stalemate is trivial for black: neither side wants to be left with only a few pieces, so initiative is far less valuable.

3. Kings can castle, but being checkmated results in a win. One must always move their king out of check, and cannot move into check.

Like variant 2, this variant also causes white some trouble, as they don't want to lose too many pieces, or else they will be trapped and have their king be forced to capture all of black's pieces.

Personally, all three variants sound really fun to me. The first one is closest to the current antichess, the third version seems more akin to being reverse chess, and the second version makes it slightly easier to win as black if white eliminates all of their pieces. What do you all think?
I think checkmates should lead to a win for the person delivering it; also king should be the last piece to be ditched.
After considering it some more, I believe the first variant is the best option. It most closely imitates the standard version of antichess, keeping its explosive play and potential to instantly win/lose any game with one bad move, while simultaneously reducing white's advantage considerably.

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