I consider myself relatively normal despite the fact that I can't burp as often or as loud as most people. This does create issues which many of you have already shared: social embarrassment or anxiety in social situations, gurgling in the throat, loud stomach noises, etc. However, I've been able to control it somewhat by being able to force these weird burp-like "things" to release the air from my stomach. I've never tried the finger in the mouth thing, but it sounds like I'm able to manipulate my esophagus muscles to produce the same effect. I'll try to describe what I do:
1.) Relax your jaw and facial muscles.
2.) Put your hand to your adam's apple and plug your nose.
3.) Now simultaneously try to lower your Adam's apple and draw air in through your nose. Of course, your nose is plugged, so you will feel pressure. So long as you can feel a pressure change (your ears might even pop) you are on the right track.
Don't worry, when doing this in public you don't have to touch your adam's apple or plug your nose. These steps are just to make sure you are doing it properly.
Now remove your hands from your face so you are back at step one. Now try step three while at the same time opening your esophogus as if you were to throw up. I can't describe how to really do this step so that it releases air, but keep trying until you can feel air being released in the back of your throat. It may help to move your whole head forward slightly at the same time as step three.
I don't know if the explanation will help, but hopefully it does! It works for me. When you get good at it, you can very very very discreetly "burp" inside your mouth with your mouth closed, and it being next to silent. I consider it a blessing, really.
As I've been writing this, I've made a conscious effort not to do the burp thing or fart and I've seriously had the T-Rex/boat-creaking noises in my bowels. Like, if I were in public they would be very audible and I'm sure I'd be running out of class beat red by now.
Last tip: I'm pretty sure that gas, like electricity, will take the path of least resistance. Meaning if you continually manipulate your esophagus or back of your throat, you should have air coming up no matter what. Keep that in mind. And good luck.