We would probably bid it as follows:
1♠ - 3♣! (5+♠ ; 10-13 BAL 3+♠)
3♥! - 3♠! (SI with shortness ; relay)
4♥! - 4NT (singleton ♥ ; RKC)
5♣ - 5♦ (1/4 ; ♠Q?)
6♠ - 7♠? (♠Q without Kings ; ♦Axx+???)
The question at 6♠ is if opener has ♦Axx or longer, or if it's Ax (singleton A is impossible as opener would've shown singleton ♦ instead of ♥ with 2 stiff Aces, or shown a second suit if it's good enough). We don't know, we only know opener has 5+♠ from KQ, singleton ♥ and 3 Aces. Chance is big North has at least 3♦ so I think we should bid the grand.

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