Improvements to endgame?
Completely agree with tonydal's 39...Rxg5. Trading rooks is your main priority.
43...Rh1+
44 Kg4 Rg1+ was another missed opportunity
rooks belong behind passed pawns, either for supporting them (where he wants to be and you let him do so) or for controlling your opponent's pawns.
Note: the above was proofed and edited Oct 30. Sorry if my earlier comments caused confusion.