Stanford 1/8

I still have hand records from SF Nationals. I was planning to post some of them, but I got sick of bridge.

Here's one from Stanford tonight

Our auction was
....  p
1D 1S
2C 2H
3H 3S
3N

We have J ATx QT87x AKJx. Comments on what to bid over 3S? Stiff J good for bidding 4S?

Anyway, 3NT

AQTxxx
Qxxx
J9
x

J
ATx
QT87x
AKJx

Opponents start three rounds of diamonds, LHO having Kxx and RHO having Axx.

I still have no idea how to play this hand. I'm hopeless at these, so I'll just present what I did. There was a common theme in the ending.

I immediately played the SJ, playing the Q from dummy, losing. :(  Small club came back, I stuck in the J, it held. Now I just played AK and another club. They broke 4-4, RHO was in and was forced to lead a heart away from the K. 10 tricks.

She asked if there was anything she could do to avoid that, and I mentioned off the cuff that if she unblocked the CQ earlier, her partner would be in to put a heart through and put me on a guess. It was only on the drive home that I realized I had missed the common theme: I have no guess if she unblocks. The unblock marks her with the HK.

Anyway, thoughts on how to play 3NT after 3 rounds of diamonds?