Back to the Back Rank II: Reshevsky-Fischer continued

Back to yesterday's question. 

Reshevsky-Fischer, Palma de Majorca Interzonal, 1970

Black to move

In this position, you may have been tempted to play 28...Qe2??  It does threaten a back-rank mate in one move: 29...Qxf1#.  But White gets to go first: 29.Qxf7+! Kh8 leads to this position:

Analysis after 28...Qe2??: White to play and win

So what's the winning move?

28...Qe1?? is bad for a slightly different reason: do you see why?

Analysis after 28...Qe1??: White to play and win

Of course, Fischer was not naïve in matters on the chessboard.  He found the best move: 28...Qf4!

White to play in the actual game:
a critical position!

Switch sides for a minute and try to help Reshevsky save this position with White (hint: a grandmaster playing White would have real drawing chances against Fischer): what would you recommend?  The most important challenge is to avoid getting mated on the back rank!