A discussion on BBF went unresolved, as each side took their view and stuck to it. For my part, I am firmly convinced, especially having run this by my regular partner and having read Fred Gitelman's agreement.
The situation, Part I:
Your partner opens 2♣, and you respond 2♦, played as waiting but GF. Partner rebids 3♦, presumably 6+ and very very strong.
What call would you make with something like ♠AJ10xx ♥x ♦xxx ♣Kxxx? (With a spade suit not good enough to make a positive response)
My view (shared by some in the debate) is that this calls for an immediate splinter (4♥) in support of diamonds. Sure, you might miss a spade fit. Sure, partner will not know that you have a trick source in spades. But, this is a critical situation to be practical. You have three controls, a stiff in hearts, and great diamond support. The question will be 6 or 7, not strain. With space at a premium, do not box yourself out of the ability to share incredibly good news.
You, instead, have ♠Qxxxx ♥KQx ♦Jx ♣xxx, so you decide to show that spade suit, bidding 3♠. Partner bids 3NT. Now what?
At this point, the debate was between 4NT and 4♦. Obviously, with slammish values and a stiff diamond, 4NT is your call. Equally obvious is that 4♦ would be your call with three diamonds and, per force, a side doubleton. This hand is in the middle. Which way to go?
My view is that 4♦ is right. Partner is known to have a long diamond suit that lacks the Jack. Give him any number of possible diamond holdings, and he almost always will be primarily concerned about whether his suit will produce to maximum expectations. When partner is known to be huge, tell him what he needs to know. 4NT will sound like a stiff to him, which will assuredly be overly discouraging.
Also, when in doubt, opt the lower option -- you will have more space to explore options.
So, you opt 4♦. What should happen next?
Presumably, partner will usually be able to cue 4♥. Let's assume that. What should Responder's calls mean?
IMO, 4♠ should show a spade control, not two top spades. This is a lopsided-strength sequence. Opener is not likely to be concerned about your spades to get to 12 tricks.
IMO, 4NT should (deny a spade control and) show poor trumps in this sequence. This would be a parallel to 3NT in a minor slam-probe.
IMO, 5♣ should (deny a spade control but show one of the top three diamonds and) show a club control.
So, you hear 4♥ and cue 4NT (no spade control, poor trump contribution). Opener cues 5♣? That should be last train, seeing if you have 5332 or 5233/5323.
You sign off.