I think I've found a 30. But I'm not 100% sure since this retro analysis stuff is so error prone. What I am sure of is that some eagle-eyed community member will let me know in due course if I messed up. Anyway, here goes:
Obviously this owes a lot to ideas by @Albert.Lang and @justhalf.
Highlight reel:
Unique checkmate is g5xf6ep#. E.p. is available here because:
a5 couldn't have moved because there are two black rooks out and no promotions used for black
black king couldn't have moved because white king would have been in check by bishop h8
Removals:
To verify that if any single piece is removed, e.p. is no longer available observe that almost all pieces are on squares a black piece could have come from. Except:
Ra4 if removed there is no longer proof that a5 wasn't moved in the last move.
EDIT: not needed, see @Albert.Lang's commentRc4 if removed white could have had another rook on e8 and the position could have been reached via 1. Re8-e7+ Kg7-f8+ 2. Re7-g7+ Kf8xg7.End of Edit
Pf5,Pg5 obvious.
Bc8 same as Ra4.
Ng8 does not invalidate e.p., but it is no longer checkmate: 1. g5xf6ep+ Kg7-h6.
Proof game:
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"] 1.Nf3 Nf6 2.Nc3 g6 3.Nh4 Bg7 4.Nf5 O-O 5.g4 Bh8 6.Rg1 a5 7.Nh6+ Kg7 8.Ng8 Ra6 9.g5 Rb6 10.Rg4 Rb4 11.Nb5 Ra4 12.b3 c5 13.Ba3 c4 14.Bb4 c3 15.Rc4 Nc6 16.Bh3 Qb6 17.Kf1 Qe3 18.Kg2 e5 19.f3 e4 20.Kg3 Ng4 21.Qf1 Qd3 22.Kf4 Re8 23.Qg2 Re6 24.Rh1 Rd6 25.Qf1 Nf2 26.Qd1 Nd4 27.Ke5 Qe3 28.Be6 Nf5 29.Na7 Rd3 30.Nb5 Nd4 31.Re1 Nh3 32.a3 Nf2 33.Rf1 Nh3 34.Rh1 Nf2 35.h3 f5 36.gxf6# *