"Strip Squeeze" isn't as dirty as it sounds

Last night in the Swiss, I picked up Qxx 9x Ax AJTxxx at all red. Partner opened 1D (10-15 HCP, 2+ D), RHO overcalled 1S, I bid 2C, partner raised to 3C, and I put us in 3NT. The S9 was led, and I saw:



It looked like nine tricks if the club finesse was on, but a few other chances if not. I put up the ace of spades at trick one (trying to get LHO to continue the suit if she won a club trick) and led a top club from the board. This lost to LHO's king, and she duly continued spades. RHO won with the king and cleared spades, but five more rounds of clubs turned her hand to mush. In order to keep all of her spades, she had to either pitch her ace of hearts or come down to the stiff king of diamonds. She decided to stiff her king, but I was able to read it and play ace then queen of diamonds for my ninth trick. Had she pitched one of her spades, I would have thrown her in with the ace of hearts and forced her to lead away from the king of diamonds at the end. Here's the whole hand: