Jennbridge: A Bidding Challenge

Playing matchpoints, both vulnerable, RHO passes and you hold:

♠  A
♥  T875432
 ♦  64
 ♣ QJ3

Do you bid or pass?  If you bid, what do you  bid?

I prefer my preempts to be sound in front of an unpassed partner, particularly in second seat.  So I passed.  LHO passed, and partner, in fourth seat, opens 2NT!  Now what?  Do you put partner into 4 hearts or try for slam?  If you want to try for slam, how would you do it?

I took the low road and made a Texas transfer of 4 Diamonds and passed partner's 4 Heart reply.  The hand has 7 losers, and I didn't see a good way to describe this hand to partner.  There are two possible ways to try for slam:  (1) transfer with 3 Diamonds, and raise partner's 3 Heart rebid to 4 Hearts; (2) make a Texas transfer of 4 Diamonds, then over partner's 4 Hearts, cue bid 4 Spades.  (1) probably wouldn't have worked, but (2) would have at least gotten partner interested, as she held

♠  J85
♥  AKJ
♦  A74
♣ AK83

After an unspecified slam try, it would be hard  to move toward slam because of the 3 quick spade losers.  However, after partner makes a Texas transfer followed by a cuebid of 4 Spades, I would bid slam with these great hearts and outside controls.

So did you come up with the winning sequence?  If you look at the combined hands, you will see that all it takes to make a GRAND slam is for LHO to not hold all three missing hearts, about an 85% chance.  Six hearts is a lock.  Yet out of 8 pairs, only one got as far as 6 Hearts.  I  think that this is a sufficiently difficult problem for consideration in Bridge World's Challenge the Champs, so I submitted it. 

Good luck!