I read 3♥ as showing values in ♥ on the way to 3N. North, if happy with his ♣ stopper can bid 3N and, if not, he can bid ♦ again. North shouldn't worry about his singleton ♠ since South bid them.
I play that 3H sets hearts and that if hearts is set, 3S is a non serious slam try for hearts. This allows us to show difference ranges by both opener and responder plus there is no ambiguity over what the trump suit is.
I think you can play it as 6♦ and either 4♣ or 4♥. Since 1♣ can be on only 3 cards, we could still easily belong in clubs.
Partner can bid 3♣ as in pass or correct. Without 4♣ but 4♥ the 2N-bidder ...