This is the reason that I hate overpairs on boards like 467 rainbow. Most of the draws that you are facing will have 8-13 outs against you (let's average it as 10 outs), so you are not a big favorite to win by the river.
With that said, you have to come up with a plan on the flop for how strong that you want to play the hand. If you are comfortable with playing for stacks with JJ here because you think that Villains might stack off with worse, then I would definitely make a plan here of bet flop and shove a blank turn.
Nevertheless, I think it is important to put your opponents on a range of hands that they would call a good-sized flop bet. In this situation, I would put my opponents on the following range if they only smooth call my flop bet:
54s, 52s, 55, 65s, 75s, A5s, 42s, 43s, 86s, 87s, 98s, T7s, A7s, 88-TT (draws/weak pairs/weak overpairs)
76s, 64s, 74s, 85s, 53s, 44, 66, 77 (slowplayed monsters)
Of course, I would only expect a Villain to slowplay a set or 2pair on the rainbow flop sometimes (often, a reasonable Villain with 2pair/set would checkraise or lead the flop because he correctly fears a straight draw). So, I would discount some of the 2pair/set combos in this range.
So, let's say that you decided to stack off with JJ here on the flop as long as a safe card hits the turn. I would recommend betting $375-$400 on the rainbow flop because there are so combo draws that have 8-13 outs against JJ here. That create a $1625-$1700 pot on the turn, leaving behind around $1400 for a less than pot-sized turn shove if a brick hits the turn. If a scare card hits the turn, I would shut down and get to showdown cheaply.
Now let's consider what turn cards are safe for us and what turn cards are bad for us:
scare cards: any 3,5,6,7, or 8
neutral cards: any 4 or A (completes bottom pair or A5s/A7s)
brick cards: any 2,9,T,J,Q,K (T might complete 89s nut OESD, but that's pretty much it)
When the Ace hits the turn, I would generally consider that to be a neutral turn card that is unlikely to hit most of the Villains' ranges. Only A5s or A7s will have improved when the Ace hits the turn; therefore, if we had the best hand on the flop, then we still should have the best hand on the turn. On the other hand, if either Villain has A5s or A7s, then we will be drawing to only 2 outs after the turn. Given that the pot is so big at this point, and that 1 or both Villains probably have combo draws, I would shove turn even on an Ace.
Summary: First, you should act yourself whether you want to play for stacks with JJ here. If you think that you want to play for stacks, then the best plan would be betting $375-$400 on the flop (because so many draws have 10-13 outs) and then shoving turn on any non-scare card.