Finding a Plan

By the arithmetic of piece value, White has an advantage. Converting the advantage is another matter. How should White proceed?

White to move

I played 33.Nf7, which throws away the advantage in the opinion of Stockfish. Nonetheless, I went on to win when my opponent managed to let a rook get trapped. Twice, my opponent offered a draw, including just before my last move.

Black to move

Final position after 45.Ne5

This game was played at three days per move and lasted two weeks. Most of my moves were made between 5:00 am and 6:00 am on the iPad Chess.com app.