With regard to bidding 6
♦ it's worth noting that you should not assume that
♦ will run for no loser.
Accept for the sake of discussion the partnership decision to play Gambling 3NT. Assuming we play that 3NT shows a "running minor", just how running must it be? Even if the partnership has accidentally agreed "absolutely solid", in reality when you are dealt AKQxxxx the suit is a strong favorite to run for 3NT purposes -- especially if partner won't sit with a void. So given the stipulation that Gambling 3NT on AKQJxxx is a winning strategy, the case for opening 3NT with AKQxxxx is weaker by so slight an amount that it would be very surprising if the dividing line falls between the two. Therefore as a practical matter, if you play Gambling 3NT at all you will not flinch at using it with AKQxxxx.
That being the case, how likely is the suit solid for slam purposes? Opener is known to have the AKQ and 4 of the remaining 10 cards, hence 40% to hold the J in which case the suit nearly always runs, but a 60% chance to be missing the J including a 1/3 chance to be missing both J and 10. In the last case it is only 35% to have a 3-3 break and no loser; with AKQ10xxx adding in Jx brings the chance to fractionally over 50% (54% that the J drops per
http://dna-view.com/suitbreaks.htm, less 2% for singleton J). The net is only about 5/8 chance that a suit that is "solid" for NT purposes will run opposite a void. (I'm ignoring 8-card suits, but perhaps in that case as well opener can and should "cheat" by opening with AKJxxxxx.)
On the present hand, 6
♦ is almost surely off the
♣A so trumps will need to run. In addition, we may have a handling problem: likely need to cross to dummy with a
♥ ruff (though the actual
♣Q is a nice bonus) and a
♠ lead could be a killer (though the actual
♠Q is helpful). Bidding 6
♦ is betting that the chance of losing a handling trick is under 20% (because 80% chance of no handling trick x 5/8 chance trumps run is 50%). I don't have a strong opinion about that; my point is just that if you bid with your eyes open you accept that a
♦ loser is substantial possibility and will blame fate, not partner, if it happens.