I'm not good at these endings, but what about 43...f4 (I anyone already suggested that, my apologies.) If 44.g4 Rg5 I think Black has some winning chances. And 44.Rxg7 Rxh5+ 45.Kg2 fxg3 looks very strong--winning--for Black

I don't understand why nobody has suggested 40...Kf6 with the idea of ...Kg5 and taking out that impudent h-pawn.

Well my idea was to play 40...Kf6 but as in the annotations I thought I'd be able to achieve that with tempo.

That doesn't change the fact that if you play 40...Kf6 right away, then he doesn't have f4 or Kh4 unlike 41...Kf6.

Like I said, I expected the rook check, in which case she doesn't have f4 or Kh4 anyway.

And what about 41. ... Rd2? That is more or less equivalent with Rb2, but has the advantage that the rook is supported by the king and a pawn. That forces the win of the pawn on the a-rank or the exchange of the rooks. Unless off course white decides to back his a-pawn from the a-rank.

But then can black start playing his center pawns.

Scott,

This woodpusher sees a possibility to really complicate whites game, maybe winning.  41. ..Rxf2 sticks out in my mind..as a good opportunity to take more control.

The plan and ideas I see here are.

1. Your e pawn is now a passed pawn with support of a connected pawn, whites is just a rook pawn

2. If there were no rooks on the board... Your king and kingside pawns shall promote the e-pawn.

3. The white king for now is fenced in by the rook by two files

4. Extra pawns on the kingside, bonus

5. If white takes your a pawn toss your rook back to the a file and now white is the proud owner of a peice of wood that looks like a rook, now purely a defensive peice.

6. Two conencted pawns on the sixth rank cannot be stopped by a rook, king or both. 

I think that move gets black going in the winning direction.

My .02