It's the bacteria (in the air, and everything else) that causes food to go bad. Open containers (or constantly openned/closed) on tables is a little different than a well seeled container sitting in a relatively cool dark place.
If you work quickly in a clean environment
, and use hermetically sealed containers (maybe something that can expel the air, instead of mason jars) and fill the containers to the lid, so there is the least amount of air as possible, you should be fine for at least a few months. Of course test before eating just in case... Usually pickled items will discolor when bad, and will probably go rancid, although that's just a rumor because I've never seen a pickled anything go bad...
Ever seen those pickled pigs feet on the counter in southern convenience stores, the ones floating around in that murky pink solution?
I know a guy that actually eats those. He can't go into a store without getting one
I've seen those jars sit for well over a year at the local store (absolutely positive it's the same jar, I checked) and probably much longer than that. That's just a screw on lid with dirty old tongs occasionally dipped in, and we're talking about pigs feet, not peppers or veggies
I'd trust some sealed and stored peppers quite a bit more than that stuff...
You could try giving them a water
bath in the mason jars per standard canning instructions. But you'd probably over cook them (like you said), and it would seem just as well do the whole process with fresh pepper/veggies to begin with.
I say try it out, worst case scenario you have to throw out a few jars of peppers and you're out $7.