How to bid a slam when partnership cannot find the best suit?
Playing 2-over-1 with a few conventions (including the serious 3nt), my auction would be something like


1d
1s
2c (this is a bit conservative but I think the right call)
2h (artificial game force)
2s (showing three cards in spades)
3s (setting trumps, showing a hand that is not bad for slam. A hand with poor controls would bid 4s, ending the auction)
3 nt (conventional. Serious 3 nt shows a strong slam try. This hand is a maximum for the actions taken so far and has good controls)
4h (showing first or second round control in hearts, denying the same in clubs or diamonds)
4 nt (asking for key cards)
5d (3 or 0 - ak in spades and a in h)
5 nt (confirms all 5 key cards and sq, asks for kings)
6s (no side king. With 7 spades, I would have bid 7 spades, as I have two tricks partner didn't know about, which must be enough to make grand reasonable)


Now north has a couple of options. They can count 6 tricks outside of spades, with a possibility of two more in diamonds. This makes me think that we should be in spades, not no trump. That virtually guarantees a fourth diamond. To make grand, we'll need six trump tricks. It doesn't seem too difficult to get there, so an aggressive north can bid 7s.