Swallowing is a common and aggravating problem with tmj. I'm wondering how you hold your head and place your tongue when you swallow. It also sounds like you might be quite tense when you swallow. And this will sound silly - but are you sure it is your jaw popping and not your ears? Another thing to look at is if you are moving your jaw (sideways) or even holding your jaw out of alignment when you swallow. Are you possibly clenching or even touching your teeth when you swallow?
These are all areas to look at and see if you might need to change how you swallow. The teeth should not touch, ever, except when possibly eating. Look in a mirror and watch your chin position when swallowing. You might have to change how you swallow, and believe me, I know how hard that is. I don't know the "correct" position for the tongue, but I had to retrain myself to hold my chin down (instead of sticking up and/or out) and place my tongue in a different place. I still have problems occasionally, but it is much better.
I hope and pray that something helps.
God bless...
Carol