I first realized that my aerophagia happened regardless of whether or not I was asleep. I realized this by setting my CPAP to a static pressure of 8, which was enough to induce aerophagia even while laying awake. I then found that gently pushing a finger or two up against my Adam's apple (right in the middle, basically just under or at the bottom of the thyroid cartilage) was enough to manually hold my esophagus shut, preventing aerophagia entirely.
My next step to make this solution work in my sleep was to build something that would do the same thing. I had a cervical soft collar (https://www.amazon.com/Velpeau-Brace-Foa...072Q9QG68/), and a padded sleep mask https://www.amazon.com/Manta-Sleep-Mask-...B07PRG2CQY) laying around, so I used one of the velcro eye pads and stuck it to the center of the collar. This is so that when I tighten the collar around me, the pressure goes ONLY on my Adam's apple, and does not distribute pressure around my entire neck, which causes a stressful choking feeling for me. I will note that the two items combined cost $53, so I would try testing with fingers on the neck before buying anything.
Anyways, I basically just wear the thing around my neck so the pad is gently pressing against my Adam's apple and I can raise my pressure up to 10 without getting any aerophagia, which is enough to give me quality sleep. It's been quite successful for about a year now, though the one issue I've had is that if I don't wear it tightly enough it doesn't work (and I don't want it too tight). This doesn't happen often, as I can "sense" how much pressure I need to put on, but it probably takes some trial and error to get it just right (would probably make sense to make some sort of marking to indicate where to put the velcro on every time to it is more consistent, but it's not a pressing issue for me now).