Yeah, by raise/folding you pretty much are turning JJ into a bluff. You make it very difficult for either player in the hand to continue with anything that we beat. I don't see the BB's shoving range including too many hands we have good equity against, but then again, we have put him in a position where he can't really flat-call given the size of your raise, so his combo draws are definitely still in his range.

It's also worth noting that since he's the BB in a multiway pot and was getting great odds preflop, his range does contain combos of 65s, possibly T6s, and maybe even T5s or 65o. He's also unlikely to lead out with just a Tx hand. You're right that UTG's range is rarely a concern since he almost always has Tx or a weak flush draw, but that doesn't necessarily mean we should raise.

Think carefully about stack sizes in these spots. You put yourself in a position here of folding an overpair getting close to 2.5 to 1. That's far from ideal. I recommend plugging your estimation of his range into an equity calculator like SliceEV, and working out how much equity JJ has against it. You only need around 29% here, and I'd imagine it's quite close either way once you include the combo draws.

One other thing – don't raise for info. You don't have to wait until he's shoved all-in to work out what his all-in shoving range would be in this spot. Raising for information is an outdated concept that shouldn't really be part of your game.