I am not fully aware of all options, but what about Ra4? it seems that we can do that, and then come back to the Ne4 line, with one pawn more for us, and a slightly better situation.
More generally, it seems a pretty good idea to use, before going to the ending, the fact that the king is threatened by many mate patterns... ( I don't know the english word for this: "battery" maybe?)
For instance:
30. ... Ra4 31. Nc1 (forced to avoid mate EDIT: NOT FORCED,) Nxa2+
then various possibilities:
two bad ones.
- 32. Bd4 is terrible for white, after: 32. ... Nxc1+ 33. Kb1 (or b2) and then bad things for white, such as A. taking d4 with rook or Bishop, and B. if he played Kb1 mate threats, for instance 33. ... Bxd4; 34. Kxc1 Ra1++)
- 32. c3 and then Nc3+ back to his place with two pawns and no tempo loss.
then the most likely move:
- 32. Kb1 and then, 32. ... Nc3+ back where it was with one pawn more and no tempo loss!, and we can do the Ne4 thing, after he plays either 33. Ka1 or 33. Kb2.
if he plays 33. Ka1, the only difference is we have a Ra4 rook instead of a Rb4 rook. If he plays 33.Kb2, we can even play 33. ... Rb4+ to come back exactly to the same position, with only the a pawn down.
notice his Knight is in a very poor position (c1). This might eventually go in even worse positions and mates, since his King is very very closed in his little corner.
So by now I would vote 30. ... Ra4, because it is at least exactly as Ne4, except that we have the white a pawn, and make his situation worse (Nc1). Waiting for comments!