A knotty problem

The scoring table demands that when looking for a minor-suit slam, we should be able to stop in 4NT, thus scoring 430 (hopefully) instead of 400 (or 630/600).  For example, 1♣ (p) 2♣ (p) 4♣ (p) 4♠ (p) 4NT is to play where 4♣ asked for keycards and 4♠ shows not enough

What about when the fit is first established at the four-level and that bid itself is not a keycard ask (or when playing kickback)?  Partner and I had the following auction this evening (opponents silent throughout): 1♦¹ – 1♠ – 2♣ – 2♥² – 3♥ – 4♦ – 4NT.  (1) 11-16 hcp, at least two diamonds, may have longer clubs up to 5; (2) fourth suit forcing to game.  After my club rebid, I showed at least 8 cards in the minors (usually 9) and therefore at least three diamonds.  After my heart "raise", I showed either 0445, 1435 or perhaps 1444 shape.

My 4NT bid was intended as non-forcing suggesting that we play in 4NT because my hand is going to be a disappointment for a diamond slam.  In fact my hand was ♠3 ♥AQT7  ♦A97 ♣KT632.  My partner thought that 4NT was a cuebid showing a heart control (since 4♥ would have been the keycard ask).

While it makes sense for 4NT to be a cuebid when our agreed suit is a major, I don't think it makes sense when our agreed suit is a minor, for the reason stated in the first sentence above.

If I was enthusiastic about slam, I could bid 4♥ (keycard ask), cuebid 4♠, cuebid 5♣.  Admittedly, there is now no way to show a heart control, but it seems to me that we gave that possibility up when we agreed to play Kickback.  How often would I have the hand with two quick losers in the unbid suit (hearts) such that I wouldn't feel comfortable going straight to the keycard ask?  Especially when I actually "raised" hearts earlier myself.

Comments welcome.