I eat absolutely everything and I've never had the need to burp to relieve gas, although, on occasions I have accidents but not when passing gas; in fact, I've never had issues or discomfort with gas, whether sitting for long periods or not.
If you're experiencing such issues, maybe you diet is the cause.
I don't believe forcing yourself to have a bowel movements will cause harm, after all, if your J pouch is empty and there"s no gas, nothing will come out, other than maybe a little mucus, unless you're straining too much, even then, the worst that can probably happen is a hemeroid.