Annotated chess game

White is absolutely correct to keep his queen. It gives him some hope, however slender of forcing events in his favour.

Great: White has no checks, and is faced with imminent checkmate.

No! Quite the wrong idea. Black has all the resources ready and available to wrap up the game in a few moves. The h-pawn is an irrelevance. In fact, after 54...Rxf5ch it is checkmate in three more moves. But Black could win the queen in a couple.

Good. If you wanted to be sure, 55...Rxf5ch 56.Qxf5 Qxf5ch would have won easily enough.

Use your checks to try and corral the king, Bear in mind the possibility of pawns or queen blocking the check. This check looks like a good one, as, to avoid the king being checkmated on e4 (...Rd4# or ...Qd4#) the King has to go to the g-file. There, ...Rg7ch will further confine the King (or win the queen if Black chooses)

Again, good for the win. But I like 50...Rg7ch. If the King retreats to the h-file it is mate in at most 2 moves; and if 51.Kf4, Rb4 is checkmate. So White's best would be 51.Qg4. Black could then simply exchange a rook for the Queen, or, maintaining the pin, weave a mating net with the other two major pieces. I can appreciate that in situations like this there are so many possibilities it is hard to know which go somewhere and which don't. What you do is look for a planned sequences of forced moves that seem to make some kind of progress. The sort of thing I'd go for here is 50...Rg7 51.Qg4 Qe1ch (or just simplify by 51...Rxg4ch) 52.Kh3 ... (Kf4; Rb4#) 52...Rh7 53.Kg2 (else White simply drops the queen for nothing after the queen blocks the check) 53...Rb2#. See how i try to make the pieces work together.