Both Deep Fritz 12 and Deep Rybka 4 evaluate this as won for White even afrter 35-move deep analysis, although I can draw easily by keeping my King where it is and using the rook to check when required. I drew this game against a player rated 200 above me.

Sorry about the error -here is the correct inverted board.

Nice job.  

However, you could have lost the game after 47.h7 Kc7??  Correct was either 47...Ka7 or 47....Kb7.

If White had played 48.Ra1 (threatening 49.h8=Q. If 48...Rxh7 then 49.Ra7+ K-any 50.Rxa7 wins for White) instead of 48.a4 White would have won.

But then you found the drawing line 48...Kb7!  

In your diagram, it looks like White queens easily after Kf5.

Oh, I see! Rh1 lets you continuously check the King.

You should fix the diagram in the OP, it is reversed. In that diagram, white has a win in 34 starting with 1. Kc4, but actually any king move wins. However, in the correct (flipped) position, black can indeed defend.

Note that any engine without a good tablebase will not be able to fully evaluate such a position. The engine knows that white clearly has the advantage but cannot know for sure if she can convert it. Engines don't understand the kind of logic you use to evaluate this position, they just calculate lots of lines.

However, you can equip your engine with a six-man tablebase (if you have tons of hard drive space), in which case the engine will know this is a draw.

white was supposed to win