It is clear that we cannot win from this position, we are too far gone to even hope for a draw. However this game has always been about having fun (at least for me) so here are some thoughts on the current position.
Firstly, f3, Bxe4 and Bf1 are the only moves I've looked at, simply because any other move loses material immediately. At this point my aim is to try and prolong the game for as long as possible.
If Bf1, then I think Bf6 is surprisingly strong, at least I couldn't find a satisfactory reply for white. (I didn't really look beyond Bf6)
28.f3 Nc2 29.Ra2 Bg5 30. f4 Bxg2 31. fxg5 Bxh3 and there is no way we survive
After Bxg2, white has the option of taking the Knight on c2 instead of capturing the Bishop of g5. One variation to this would be black playing play Bc5+ instead of Bg5, keeping the option to play Be3 later, pinning the Queen. The thing is I'm not 100% sure black will play Nc2 in response to f3.
Lastly, Bxe4 doesn't not look as bad as I originally thought, unless I've missed something. After Qxe4, I was looking at cxb5 whether black recaptures or not we could then play Nb3, protecting the Bishop on d2 and freeing the rook on a1. It doesn't look like it would be easy for black to challenge the Knight on b3.
28. Bxe4 Qxe4 followed by 29. cxb5 feels like a slightly clearer (with less complications) path to me but I could be wrong.
What do you guys think? Let me know if I've missed anything
EDIT - Sorry I was being sloppy with the 'whether black recaptures or not' bit
after cxb5, Bg5 is too strong to ignore
and calls for f4 instead of Nb3. I still think Bxe4 followed by cxb5 is ok though. We will probably lose the f4 pawn but it feels like an acceptable trade off for me, remember we have a pawn on b5 that has not yet been recaptured in this variation.