Great ideas, thank you very much! I missed Bc5+. I was also very surprised when he played Ng4 - I guess the idea of threatening mate in one enticed him.
Maybe he felt compelled to play Rxh2+ because otherwise Ng4 would be pointless - I know it can be difficult to admit a mistake. Oh, and I just saw the idea of Nxh2 instead of Rxh2+, which I find quite interesting as it threatens Nf3#, Nxf1+, and Kxc5 all in one. In fact, I can't even figure out what I would do if he played that.
27.Rf3 is an interesting idea that I didn't consider at all there - I think I should look at quiet moves more often in the middle of King hunts. I'm always too quick to play the first "attractive" check, if that makes sense - a check that draws the King in closer and puts it where other pieces can check it. 27...c5 can't be good since there's 28.Ra3+ Kb4 29.Ba5#. I guess there's also nothing in 27...b6 and 28...c5 since the a8-Rook gets trapped by the Bishops. The only attempt at defense I can think of (and I'm not at all sure it works) is 27...Rh6. The idea is that after 28.Ra3+ Kb4 29.Be7+ (or Be2) c5 30.Be2 (or Be7) Black can play 30...Rc6 to defend c5. Also, the Knight is no longer tied to the defense of f2 and it's OK if White exchanges on g4. 28.Be7 Ka5 and the King tries to escape to b6. It looks rough after 28.Be7 Ka5 29.Ra3+ Kb6 30.Bd8+ Kc5, but I don't see anything better for Black and White still has to prove something here since Black's light-squared minors are both defended and the discovery doesn't seem to win material. Is there a mate somewhere in that position? The Black King gains a lot of squares if it steps to d4, but I feel like there must be a mate.
Another blitz game... I ended up with his King coming over to my side of the board, but I only had a Knight (which I had to trade soon), two Bishops and two Rooks plus some pawns to attack with. Was it enough? I've put some lines in, but there are so many other options... Do you think I was won from the start (by which I mean move 15) or did he have a defense? Perhaps I was won but I let it slip away at some point, but he returned the favor?