Well, as I originally saw this as standard Chess with a peculiar position, I allowed each side to promote to Queen. If one sees it as an independent Chess variant, it is indeed an interesting idea to fine-tune the odds in this through the promotion.

Now that I am converging to an engine that is pretty good at this, (compared to normal Chess engines), it seems that black has the better chances after all. The path to a black win almost always goes through trading a Queen for two Knights. With two Queens vs four Knights it is usually an easy win. It is very difficult for white to avoid a Q vs 2N swap, (for which all Knights must remain doubly defended, or defended by a Pawn), keep all its Pawns defended, and prevent creation of a passer, and in the long run it will not succeed.

The development advantage of white also is a bit illusory: although the Knights can be developed in a single move, you have many, and to develop 6 Knights takes 6 moves, comparable to the 5-6 P+Q moves you need to develop 3 Queens. The Knights start in a very vulnerable position, all undefended, and the array has some Pawns undefended as well. Even with a more favorable array, (moving 4 Knights and 4 Pawns one rank forward) white scores only 20%, now that black uses a proper strategy.

I guess, however, it makes little difference what black promotes to. Even limiting him to a Knight, would make promotion a sure win. In practice white never allows promotion; it gives a Knight for the passer. But loss of a Knight is always fatal.