N:9 B:9 R:8 Q:9 P:14
After I'd posted 4 problems, Rewan Demontay revealed that actually work on this had continued in another forum a couple of years ago, and better problems were eventually found, but never posted here.
To avoid more people wasting time like myself & poor @happystar, I have posted the 4 all-time records here, so that people can see. In my opinion, none of the four are likely to be improved.
My only novelty is a new 5th case: "dummy pawn" (1862 rules, pawns can stay unpromoted on the 8th rank). See https://chess.stackexchange.com/questions/21212/when-if-ever-was-it-a-rule-that-pawn-promotion-was-optional for details of this amazing rule. So this is how Queen Victoria would have played chess in the latter half of her reign :) Maybe someone can improve on record? There are a number of different matrices possible.
All five White promotions can be forced uniquely (with multiple Black responses allowed - this is normal self-mate protocol). All these are proved sound by Popeye solving software.
Note that all 4 of the previous problems still remain even if dummy pawn is available as an additional promotion target.
N: 9 units (Hauke Reddmann)
B: 9 units (Rewan Demontay)
R: 8 units (Rewan Demontay)
Q: 9 units (Hauke Reddmann)
P: 14 units (Laska)
