Six or Seven? 5NT bid ***

In last week's team game, I picked this beauty up in third seat:

♠  KQx
♥  AKJxx
♦  AJxx
♣  x

Jenn dealt and opened 1 Spade!  I immediately thought of slam, possibly a grand.  I had a good fit and possible source of tricks.   I decided it would be best to take the wheel and get as much information as I could.  How would you proceed? 

I started with 2 Hearts, to create a game force, planning to bid spades next to set the trump suit.  Jenn responded 2 Spades, which by our agreement showed a 6-card or longer broken suit with unlimited values.  [An alternative approach, favored by Lawrence and used in Bridge World Standard, is to rebid 2 Spades to show minimum values, perhaps with only 5 spades, so that 2NT or 3 of a new suit would show extras.]  Now I bid 3 Spades to show the fit and slam interest.  Jenn replied 4 Spades, showing a minimum.  But even with her minimum, a grand slam wasn't out of the question if she had the right cards.

I checked for aces with 4NT, and she replied 5 Hearts, showing 2 keycards without the queen.  Now I tried 5NT, confirming that we had all the keycards and the trump queen.  This is an invitation to a grand which asks either for specific kings or acceptance with other suitable cards.  [If, for example, Jenn was looking at the heart queen, she might accept on the theory that I most likely had the AK of hearts.  If I only needed the heart king for seven, I would have bid 6 Hearts, not 5NT.]

Jenn replied 6 Spades, which denied any kings or interest in a grand slam.  I gave up and passed.   Jenn got a diamond lead and looked at:

♠  KQx
♥  AKJxx
♦  AJxx
♣  x
 
♠  AJ9xxx
♥  x
♦  xx
♣  A10xx

I can understand why she wasn't anxious to cooperate in a grand slam try!  She had only 9 HCP, but nonetheless a solid 1 Spade opening bid.  She played it as safe as she could to make six:

Diamond ace.
Heart AK pitching a diamond.
Club to the ace and club ruff low.
Diamond ruff.
Club ruff with the queen. 
Spade king.
Diamond ruff (LHO followed up the line on the second diamond).
Spade AJ drawing trumps.
Concede 1 club, making six.

Jenn told me later that if she were in seven, she probably would have made it.  Spades were 2-2, so she could have ruffed another club with dummy's king and drawn trumps with the AJ.  This would have required either 2-2 spades or 3-1 with a stiff ten, plus getting back to her hand once more with a ruff, risking an overruff.  Surely not worth the risk playing IMPs when the contract was 6, not 7.  +980 pushed the board.