It took me 4 months to feel mostly normal. I know you're only 3 months out, so I'd wait before doing anything drastic. Your only recourse for food getting stuck is probably dilation, and with a floppy wrap you really don't want to do that! It would negate the whole idea of strengthening the sphincter.
At only 3 months out you are probably still experiencing gas. I have it still too and mine was done in late October, so I'm only 4 1/2 months out. Yes, you may be ABLE to burp, but you probably don't burp normally yet, or even when you have quite a lot of gas. Maybe never. I burp some right after eating or drinking, but there's always some left. I can tell because it's quite noticeable when it starts gurgling around the large intestine ... and beyond.
To limit the gas problem try eating less starchy foods, including vegetables. No, it won't do much for the swalowed gas, which is what you're complaint is about. It will, however, limit some of the bloating in the lower intestine, which presses on everything else. Google for info. Rice does NOT cause gas, so you can start with replacing bread and potatoes and anything with starches with that.
I've found that losing weight helps too. I was already at the top edge of the "normal" for my height. When I read the operative notes I noted that the doc complained of lots of fat in the mediastinum (the area where the esophagus goes up into the chest (and where they had to go to pull down my stomach which was stuck in my chest after the wreck). Since I know that means I also have lots of fat around my heart, I started working on losing a little more to get the the middle range of weight for my height. After taking off another 10 lbs I have lots less bloating and pressure from my stomach, even right after eating. So it's working.
This is the kind of stuff you are not likely to hear from your gastro doc, or I wouldn't bother posting. Good luck and God Bless.