Nice question. Here's a slight variant of your construction which saves one move. The final position is almost the same, but there's a pawn transferred from a4 to e5 (which saves one pawn move).
[Title "Proof Game In 46.0 Moves"]
1. a3 Nc6 2. Ra2 Na5 3. Ra1 Nb3 4. Ra2 Na1 5. Nh3 Nf6 6. Ng5 Nd5 7. Nc3 e5 8. Nb5 Nc3 9. Nd4 Nb1 10. ...
An improvement for n=4, building on Rewan Demontay's answer:
[Title "n=4, 26 pieces"]
[FEN "2Rnr3/PP1PP1PP/RKQ3rk/7B/5n2/6Bb/pp1pp1p1/3NN2q w - - 0 1"]
The trick is to replace some pawns by knights or rooks to keep the position legal with less necessary captures.
This version has more pieces and less pawns, so I think building a proof ...
Sorry Hauke, but I can't get a headache this time. I've already commissioned n=1 n=2, an n=3 over on the Puzzling Stack Exchange. However, here the positions from the accepted answers for reference. The way I see it, I technically am the one the who got the gears rolling that produced them. Thus, I "found" them in my archives. Either way, I've beat ...
This solution finishes with White's 54th move. Every White move other than the early e-pawn moves is one of the following:
A pawn capture by a Queen moving from the eighth rank
Placing a piece
Placing a pawn on the seventh rank
1. e4 d5 2. exd5 c6 3. dxc6 a5 4. p@c7 Ra6 5. cxb7 Rb6 6. p@a7 ...
Welcome to Chess Stack Exchange, Robert Linsley! I am a chess problemist myself, as others here are, so I can help you out. By stating that it is legal, you already ahead of most people! Chess problems are not entirely strict and you can compose anything you wish. However, there is a "Chess Codex that has been formed over the years as a guideline (no ...
After playing around in Lichess's analysis page, I found a mate in 10. Throwing the moves into chess.com's analysis page provides further confirmation. It has a few wholly unique lines, and some dualed ones, making it reminiscent of a chess problem per @Hauke Reddmann's above comment.
[Title "#10 After 3 Moves"]
1. e4 d5 2. h3 ...