Hm.
In the second game between Web and Book, as Book I think I would have cut my losses with 29. Qc1 instead of 29. Qa4.
Offer that queen trade; support the pawn with the rook. Could be able to force a rook trade, and with some solid pawn-king play, could force Web into King vs. King-Bishop and tie the match.
Just some very rough speculation, though. As I said, I'm pretty rusty.
He was running low on time. He had to force me into a mate or lose, as I wouldn't have been able to lose. If he had played 29. Qc1, I would have played Rc8. He'd have lost the passed pawn at that point, as Qxc5 would be met by Bxc5, protecting the Rook, the lone pawn and threatening his pawn. Not only that, but not taking the Queen would end badly for him. Once I connected my Queen and Rook, I could threaten checkmate or a material advantage.
The move I thought he should have done was 21 cxd7. It has a very nice forcing move after 21...Kf8 (21...Kd8 22 Nf7#) 22 Qc6
At this point, the black queen finds itself under attack, losing the attack on the Knight at c3, and forcing itself to either get support, or move.
Seeing as how White wants the Queen gone, he's willing to trade up. 22...Qxc6 23 Nxc6
Now Black can't threaten the Pawn. Bb5 is blocked, Ra7 is blocked, Rd8 is blocked. The only move left is
23...Bb7
Followed by
24 d8=Q Bxd8 25 Nxd8 Rxd8 losing the passed Pawn, but maintaining a slight positional and material advantage. (Not 24 Ne5 as 24...Bxb4 pins the Knight and loses another Pawn for White, plus opens up the Rook for attack)
Now, if Black refuses the trade, by Qd8 or Qb7 Black faces some hard positional problems, like lack of Queen maneuverability and having White bring in his Rook. It gets really ugly, since black can't break the attack.
And as I'm no expert, what I say about this might very well be wrong, but that's what I see. And I have no chess engine to check against right now.