On the e.p. convention:
In a sense, this composition is "over the top". It shows positions where you can either prove absolutely that "white can capture e.p." or that "white cannot capture e.p." whatever the game history. Such requirements are sometimes made for purely retro-analytical problems with assignments like "prove that Be8 is promoted" or "what were the 3 last moves?".
Such requirements however never exist for problems with "forward playing" assignments like "white wins". Though solving certain problems requires a degree of retro-analysis, missing properties are filled in by "conventions" and need not be proved. The only use of retro-analysis is to establsh whether or not conditions exist that contradict the conventional assumptions. For instance, you may be able to prove absolutely that white cannot castle or can play e.p. while the conventions prefer the opposite assumptions. It is no use though to prove something absolutely that agrees with pre-existing conventions, like "white has no e.p. right". This is what I meant by "over the top".
In many common endgame and problem diagrams, it is possible to play e.p. somewhere on the board. We would lose tens of thousands of composition (and game puzzles) were we to require the composer to "prove" that e.p. is impossible. The current convention that e.p. is disallowed unless one can prove otherwise, is therefore the only way to go. So "the proof that white can win" does not imply "the proof that white can win in all game histories".
) for me to keep up...
As is, however, it must surely be impossible to satisfy such stringent criteria with a queenless position. Remember, you'd need ALL 4 positions with a White queen in place of rook/bishop to be legal when e.p. is illegal but illegal when e.p. is legal, while the original position having both rooks and both bishops remains legal when e.p. is legal but illegal when e.p. is illegal. It's hard enough to make all of that work, while simultaneously ensuring that all positions will actually have the desired win/loss outcome, when you can trivially prove the occurrence of a queen promotion in the alternative positions. If there's no obvious queen promotion, the whole thing simply devolves into a topic exclusively for professionals.
I am a professional in this field and I wouldn't say it is impossible a priori though I admit it looks quite difficult. I wouldn't use the e.p. propery but the castling property. The justification for "losing" would have to look something like this:
With a queen replacing either of the four units involved one would need to prove that either (a) a black castling right exists that did not exist before, or (b) a white castling right no longer exists that did exist before. Second, the increase of black potential relative to white potential should be convertible to a black win in spite of the presence of the white queen. Most likely such a construction would involve "promotions disturbing castling rights" which is a well known device.
Even when it does not prove possible, it may still be achievable with just 2 rook substitutions or another reduced implementation. Still an interesting task.