?! While the game is heavily in white's favor, Black should try and keep his pieces on the board and try and counter-attack. Either that or resign. I understand wanted to learn until checkmate, but why not make White fight for it?

Not allowing g4 freezing White's Kingside pawns.

Now Black either trades rooks or loses another pawn. Black, though finds a different path, but it is a rocky one and ultimately worse than trading rooks.

?? Missing that White can get back in time to win the pawn.

The rest is a matter of technique, since the Black king is cut off from the a-pawn.