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Followups after shape resolution

This hand occurred in a recent sectional(-like) pairs game in France:

North
AQ972
Q92
9
AK64
South
KJ3
AJ7
AJ7
QJ52
W
N
E
S
1NT
P
2
P
2
P
2NT
P
3
P
3
P
?

At the table we didn't have firm followups in the fitted case after 2N so the actual auction went 2N (forcing) - 3 (fit) - cuebids - keycards - 6N which was already good enough for all the marbles, but clearly you want to be in 7.  We had agreed that a non-fitted opener starts with 3 over 2N, which gives responder just enough room to shape out his 5431 below 3N (2N is forcing because we show all 5 invites via Stayman-then-2); we later realized that we could just let a fitted opener bid 3 over 2N and again let the responder shape out.  In that case there are tons of space and we can e.g. continue

1N-2

2-2N

3-3 (fit; 5=3=1=4)

4-4 (optional KC in ; positive with 0/3)

and now opener just needs to check for the Q to bid 7.

Still, I was wondering whether the BW readership has suggestions for slam auctions like this, where shape is resolved below 3N but there are multiple strains in play (here, , , NT) -- what bids are to play or invitational, what bids are asking (e.g. we are not on a very firm footing as to whether a later 5 would ask for the Q (using the standard 3rd round control ask following BW) or just an attempt to play in a higher scoring strain), whether we should just show control points and use some fancy denial cuebidding approach (which I have only briefly read about), etc.

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