Being UTG is not an ideal position in the sense of having to get 8 folds, or win a flip. However, the blinds are about to hit you; and you are unlikely to get a hand that good on either of the next two hands.
If you fold, you can expect to either (a) have to shove a worse hand on the next hand from the big blind, or (b) to fold both the BB and SB, at which point your stack will be even smaller (6,700-1,600-200-800-200 = 3,900).
With 3,900 you can see six more hands for 200 each. But you will have even less fold equity than before, and will be bleeding 200 per hand. If you shove with 3,900 or less, you are sure to face multiple callers unless someone isolates. You’re going to have to pray you pick up a better hand than AJo in the next few hands, and there are only about 18 or 19 better starting hands out of 169 possible combos. If you hit the big blind a second time, you’re going to have to get all in with a random hand.
With 6,700, you have a least some chance of folding everyone out, or getting heads up. With blinds and antes there is already 4,200 in the pot. Even if you get called by a better starting hands (mainly pocket pairs, suited aces, some Broadway combos), you’re still good about 40-45% of the time against that range. If you think you have even a little fold equity to add to that, you have a decent shot at almost tripling up.
Meanwhile, the other players (as has been pointed out by others) are surely mindful of how short you are, and are likely to let you get blinded off, or hope one of the big stacks pick you off. In that sense, you may not have to fade so many people, as you’re probably only getting called by the 1-2 biggest stacks or someone who happens to get dealt a monster.
Since your next smallest stack is more than twice the size of yours, and given how short you’ll be when the blinds hit you the next hand, I would go with the AJo and just accept the consequences.