I wouldn't use a fit jump on this suit either. I don't think having such a wide range of suit quality for a fit jump helps partner to make the right decisions. I'm not really happy with any of the bidding options, but would probably go for 2NT here as this is a pretty decent spade raise.
I would open a 15-17 NT, as otherwise it is impossible to describe the hand properly. Presumably the only worry is wrong-siding a possible 3NT contract as partner may hold something like K x spades?
Playing SAYC, i expect: 1♦, 1♥, 1♠, 3♥ 4♥, p , 5♣, p 5♦, p , 5♥, p 5♠, p , p , p So end up in 5s. South will not be prepared to bid the slam with such bad spades, and North knows south has A!h and not K!d from this auction.
3NT seems less likely than 4S to me. If pd puts down a broken spade holding, like K J 10 9 x x x how are you going to set them up in time? Even if he has better spades without the A, if they lead a club you are down when the spade game is v likely. Plus, how are 3 trumps going to split 4-1? Unless your usual pd opens 3s with only 5??
I would blame East. After West's redouble, the opps can't be let off to play 4c undoubled. With the vulnerability and such good spades, I think it is clear for East to bid 4s. Pd should be able to provide the 4 tricks neded, sitting over the overcaller.
I play a similar structure to this as part of Benji Acol. But 2c is used for the hand you describe (actually 8 tricks in a major or 9ish in a minor), with 2d as a "normal" 2c opener. Big balanced hands are then opened either 2NT for 19-20 (!), 2c with 2NT rebid for 21-22 and 2d followed by 2NT rebid for 23-24. Responder (nearly) always relays to 2d after the 2c opener to find out the suit / NT. One drawback is with a really big hand with hearts, you are already at 3h once you have shown the suit.