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I may well be too pessimistic; per the OP's auction, it felt like we had got very high and I still didn't quite have a feel for partner's hand, so I thought it sensible to play in the "safe" 9 card trump fit. In favour of no-trumps are the long side suit, double holds in at least 3 suits, maybe 4, and also the (original Jacoby) auction has given very little help to the defence - so if there is a killing lead, they may not find it. I certainly wouldn't begrudge anyone a top board if they chose 6NT, and I agree that I would be worried that many in the room may have opened partner's hand 1NT, after which 6NT seems very likely to be bid. I'm still not sure it's making though, so I'd probably stick to 6S.
I agree that 5-3-3-2 hands seem more likely to be good for either grand or 6NT since partner likely has 3x hearts. My main problem with the auction was that I wasn't clear what "15-17 no shortage" might mean as a response to 1S-2NT and I deliberately didn't include 5-3-3-2 hands because partner didn't open 1NT. Partner has at best QJT9x in spades, so even die-hard 1S bidders with that shape would be tempted to open 1NT given the slow winners in the long suit.
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Partner has lots of points in the minors, but seemingly a doubleton in one of them. KQ doubleton is hardly out of the question.
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Even if you begin 1S-2H won't no-trumps still be bid from your side? Genuine question, it seems more likely that I'll be the one bidding 4NT or deciding to bid 6NT if we've avoided it up till then? I agree with an earlier poster (TWO4BRIDGE) who said that it's the player with the kings who should go ace-asking, but if that isn't the strong hand, it can be difficult to persuade partner to do it.