problem A:>> (Naturally) The mentors have convinced me that dropping 3NT is an underbid. They propose that pard has FOUR spades, not Kx or Kxx, else there would be a minor to bid first or a 13-pt neg couble, if 4-4 or 4-5. Now, if we put Kxxx, 10x, AQxx Axx across from my AQxx, AKJxx, x, Kxx, that leaves the overcaller with an awesome Jxxxx (JTxxx?), Qxx, KJx, QJ. Asking partner if he has more than such a 13-count, or a 13-count with some kickers [ like major tens ] requires that the overcaller to have even uglier an overcall, but so be it. Raising 3NT can't hurt even though "I know" he will not have a drop extras. Changing my problem A from pass to raise (4NT).
As for "no choice-1NT" on problem B, I am standing firm on this one. I cannot ever remember bidding 2C on this or similar auctions in 45 years, which for me is more in the "rescue/ obstructive" category. Redouble is fine, but it will only led to a swamp of forcing passes leading to flailing guesses UNLESS pard has a hand that knows exactly what to do with a free 1NT after opps' double. Redoubles don't make any money when neither of us will be having 4 in whatever opponents slink off to, so it is the 3--3 majors that rule it out for me-- not the 'missing' 10th point.
problemD:>> How do we get to PLAY 2D in our 62-2 [1?] diamond fit? the good old way whick is to bid respond 1NT, and change 2C to 2D is OUT, thanks to BART (see _____'s research above). So, hat leaves me with the passed-hand 2 diamond bid. I am told that if I BART this hand, and pard comes through with the 3rd bid of 2 Hearts, I cannot be SURE that that shows three (wtf??) besides which these are not dream cards to be playing a 3-4 trump contract, I don't recall digging this far down for a 2-level response before, but look -- it IS 2 points shy of a sketchy one-opening, so, 2D is my vote.