How Many Pawns for a Rook?

The diagram below shows an endgame position I reached in a recent chess960 game. I was playing White and although it looks like I'm down boatloads of material, I'm about to recover some of it. Looking at the material on the board, it's one of the most unbalanced positions I've ever encountered.

After 26...Rg8-c8

The game continued 27.Rxg6+ Rc6 28.Rxc6+ Kxc6 29.Qg6+. Here I was expecting 29...Kb7 30.Qxg7+, when White has a Queen and six Pawns against a Queen and Rook. The game was a correspondence game where engines were permitted and I had spent considerable time studying this position before deciding to play the line. The further variations went beyond the horizon of the engines I was using, so I was on my own to make an evaluation.

• First observation: Black is going to recover at least one Pawn, maybe two.
• Second observation: The White Pawns are too far back to present an immediate threat to Black.
• Third observation: The Black King has no cover and is exposed to long sequences of checks by the White Queen.

All in all, it promised to be an interesting endgame where any result was possible. After 29.Qg6+, my opponent played 29...Kb5, and offered a draw. I realized that as long as he didn't play ...Kb7, White has nothing more than a perpetual check by the Queen on the 5th and 6th ranks. I reluctantly agreed to the draw and moved on to my other games.