Here is where I got tunnel-vision and started to move irrationally. An ice-cold Bishop interposing could easily have solved the problem.
Not a Yet a Killer
25. h3 is an odd instinct to have, I guess you want to create luft for the king but there's no threat to the back rank and d6 is a very important pawn.
On move 27 I'd just play Bxf7+, after Qxf7 Qxf7+ Kxf7 Nd5+ I'm winning c7 as well and will be up a rook and two pawns. If the king moves instead there will be Qd5+ if it goes to d7 and a discovery against the queen if it steps onto a dark square.
I realize you had a way out of the perpetual but I think the bigger lesson here is not to expend effort protecting assets you don't need. If I tapped you on the shoulder and said "would you be willing to lose this bishop to get the queens off" you'd look at the board and say "yes". But with Bxf7+ you are ruling the move out without asking that question.
The road to become a mating "Killer" goes by simplification. Start by "killing" the Queens, and rely on your material superiority. Most probably it didn't even cross your mind how much stronger you were in this position.
Simplification first - THEN checkmate!
They say that it's hard to win a won game. I absolutely agree.
Here I was absolutely winning, until I moved into a Draw. From a roaring Lion in the middlegame, I suddenly turned into a soft kitten in the End.