Last but not least, I exactly thought about the same Draughts variant as you, the player who promotes first wins.
My interest was based upon solving this variant.
At least only man-based DBs are required, and this might help.
I don't think it can be solved, but don't let that stop you
I looked at a couple of games, with endgame tables but without a tuned eval, and the scores were small for a long time. Then at some point, the loser has to give away material to (pointlessly) postpone the loss. It snowballs for a few moves before an exact result is announced. The same thing happens in chess with deep mates: they are usually first "announced" as material gains.
Othello is likely solvable thanks to a combination of factors:
1) fixed game length
2) most moves are bad => only 1-3 playable moves in a given position
3) very accurate pattern evaluation, especially late in the game
I don't see 2) in any draughts variant, in particular in the opening; this is a major obstacle to solving. Also, the number of moves before search can see the result seems too large. However a possibility remains: maybe there are many move sequences, but few intermediate positions, say 40 plies from the starting position, with reasonable play from both sides.
I should have a taylored eval in 1-2 weeks; I'll let you know if this changes my view. In any case, it's a variant without draws so every game is exciting. There's also a chance that search plays a more important role; maybe the endgame is chaotic. On the other hand, there is the risk that this variant favours one of the players even without perfection.
Regarding endgame tables, I simply reused my previous code. The builder doesn't know that a draw is not possible. I easily created tables for upto 7 pieces in a few hours, and 8 looks possible. My generator is RAM-only and has no slicing: it won't be able to go further with a normal machine. I guess that, if you can build draughts tables for P pieces, you can do it for P+2 in this variant.