I can't give an exact DTM answer, but this one will be off by only a few moves. If you replay the Syzygy line, you will see Black can only annoy White with countless stalemate shenanigans, but White will finally get Pg6 at move 48 (phew), closely making it within the 50 move rule. Since anything DTM strategy which may be globally faster surely is in danger fail due to the 50 move rule, we can safely assume the play is optimal for White, leading to e.g. this position (BTM):
[FEN "8/5NK1/6R1/6Pk/8/8/8/r7 b - - 0 1"]
This can already put into a DTM tablebase. I only have Shredder Nalimov; Black must very fast sacrifice the rook, so 16 moves seem to be DTM. So I think I can safely say DTM #65+-5.