Problem A
After reading all the previous wisdom, can I have a go?
Simple analysis:
I have a good 17 and partner must have at least a good 14. That makes 31. So invite with 4NT.
More considered analysis:
We need to balance a credible 3NT by partner against a credible 1♠ overcall by West. If we give partner ♠Kx only then we must expect running ♦s. Say
(a) ♠ Kx, ♥ xx, ♦ AKQJxxx, ♣ Qx giving West at most ♠J109xx, ♥ Qxx, ♦x, ♣ AJxx. Not much of an overcall. OTOH if we give partner
(b) ♠ KJxx, ♥ Qx, ♦ AQxx, ♣ Qxx, then West could have ♠ 109876, ♥ xxx, ♦ KJx, ♣ AJ or
(c) ♠ KJxx, ♥ xx, ♦ AQxx, ♣ Axx, then West could have ♠ 109876, ♥ Qxx, ♦ KJx, ♣ QJ
Opposite all these hands we can make 12 tricks. Trust partner has got his bid and not the opponents. So go for 6NT.