Underbid Again

As promised a hand, This came up in an OK-Bridge Tourney, playing with a fine pard with whom I don't have a lot of agreements. I pick up (Imp Pairs format; Opps Vul,We're not)

S AKQ7652
H
D AJ4
C Q65

And the dealer, on my left opens 2H, passed around to me. Now I can make the practical bid of 4S, or I can try some esoteric strength showing parlay of double/cuebid/4S or I can trot out 3S, which over an opp's preempt is a strong jump overcall. Of course, due to not having had any discussions with partner, I don't know if partner is on the same wavelength as me on that, one assumes that a good player would but many a slam has been played in 3 when someone assumed their partner was interpreting correctly.
I immediately rule out any sequence that starts with double, since hearing pard pass for penalty at light speed isn't on my agenda for this hand, and eventually decide on the practical 4S bid. Which buys the contract, and when the opening lead of the Diamond 7 hits the table (squealing "I'm a stiff" loud enough to be heard 2 rooms away) dummy hits with :

S 43
H QJT4
D KQT983
C K (my hand repeated for convenience)



S AKQ7652
H
D AJ4
C Q65

Trumps behave and I claim 7 about 2 milliseconds after I've pulled their's. It takes a 4-0 trump break to hold it to less then 12 tricks and that wasn't happening today. The question is ; Is 6 biddable by any means other then someone shrugging and guessing? I think some pair's , armed with actual understandings should be able to. I suppose that over 3S setting S's in stone as trumps, a D bid by pard followed by the crucial club control bid might do it...something like


2H P P 3S
p 4D P 4H
X 5C P 6S or maybe 5H trying for 7 if pard's club control is the Ace?

This seems like an awful lot of cooperative bidding from pard on his actual hand. Meanwhile back in the real world my "practical bid" of 4S making 7 netted a practical score of -1.77 imps.
66 scores with 16 pairs reaching a slam,7 in D's and 9 in S's. And so it goes.