Ok, I tried to cover various stuff.
Maybe 59...Rd1+ is better in your 54...Rc2 55.Qe8 Kg7 line. It is like the same position I had.
That is not the continuation I meant. I know it can be confusing. So I added the continuation. Also 60...Rb1 instead of 60...Ra1 and the rook can go to the back-rank.
Oh, well I just tried, and chess.com's depth 15 SF isn't showing an overwhelming score in all of these, but mine at home was showing either mate or something like +80.00 in all of these.
As the worlds 3rd strongest engine, I can assure that the position above is a win for white.