How should this game have continued?

In this game, I hung my queen and resigned. I had actually seen that the move would hang the queen, and mentally rejected it. Then, apparently, I forgot that I'd rejected it since I came back to discover it was indeed the move I'd made.

What I "intended to have done," so to speak, was Qg5. I feel like I was doing pretty well (especially against someone rated so much higher than me) but to be honest I didn't see a clear path to victory.

Was there one?

I would have preferred placing the queen on the f-file actually. Load up on that vulnerable open file!

I couldn't see how to do anything with it in light of white's Qc2. Then white moves to Qd2 and he's protecting the f file and the passed pawn--albeit the queen is now doing double duty but I just couldn't see what to do with that.

I wanted the queen on g because it seemed like by advancing her later to row 3, I'd be attacking both f2 and g2--a flick of the rook puts a checkmating attack on the g file--but I couldn't really read it out.

It seems like I should be able to do something with my queenside pawns while I've got all his pieces tied up, but again, I just can't read it out...

That's just it. White's queen is reduced to protecting that square. In a position like this, you don't have to force a win -- it'll come. You can then bring you king into the game or even push pawns to gain space.

One idea that comes to mind is 26... Qf6 27 Qc2 Qh4 28 Qe2 e4.  Now the idea is Qg3 followed by Rf3 picking off the e-pawn.

I don't think you really have to be too concerned here about the d-pawn, because with all of his pieces tied up like they are, he really can't push too much oomph behind it.

Bringing up the king didn't even occur to me. I think that's the insight I should have had.

I think it's possibly a bit early to bring the king out into the center.