This is the closest game I've ever played in a losing cause.  I play the Queen's Gambit as White and the extra pawn leads to a lost game for myself.  I've posted the whole game, but I'd really like help with the endgame, which begins at move 23.

a few comments on your notes:

9 ... Ne7! Nf6 would lead to the tempo-winning e5

actually, 9...Nf6 10 e5 would be strongly met by Nd5, forcing your f4 bishop back to an ignominious spot on d2 to protect the c pawn. in addition to being tactically suspect, e5 looks like a positional blunder, hemming in your dark-squared bishop, activating his light-squared bishop, and handing his knight the fantastic d5 square in perpetuity.

19 e5 Opens the long diagonal

yes, but it renders your dark-squared bishop almost useless; he doesn't have one, so it's no problem for him. moreover, you're offering--almost forcing--a trade of light-squared bishops. your bishop pair is your only real compensation for the pawn minus; you shouldn't be in any hurry to give it away. as above, too, e5 gives black's knight the beautiful d5 square for keeps.

23 Qf4? This is a key mistake. It trades into an endgame that is bad for White. Bad bishop, and an extra pawn on the queenside. I have a slight advantage on the kingside but never get an opportunity to advance the pawns very far.

agreed, though I don't see what meaningful "advantage" you have on the kingside. a little more space, but that's about it. but trading queens when you're down material with no compensation is certainly a bad idea. Bf4 (with tempo!) followed by Bc1-a3 & the ownership of the a3-f8 diagonal & control of the dark squares might be compensation enough for the pawn.

additionally, I'd say that after 35 ... a2, it looks to me like black has no way to stop you from marching your king to b2 & forcing the win of the a pawn. after 36 Kf5, I think you're dead lost--the c pawn will go & with it the game. your king's desperately needed on the queenside; he belongs there, not chasing chimeras on the kingside.

Thanks for taking the time, unferth, I really appreciate it.