I looked up past threads on this issue and the wiki on this, and the general idea is that if you adhere the tongue to the upper mouth (interior roof) behind the upper teeth, causing a seal, it would block any air to get into the mouth. Since, that is the path of air entry.
The trick is getting in the habit of keep the tongue up there. So, even when not sleeping, keeping the tongue in that spot will make a habit of it. Also, when trying to fall asleep to be mindful to keep the tongue there.
This actually worked for me (so far, crossing my fingers it's consistent), and it seems like as long as you are constantly mindful in keeping the tongue there throughout the night, I don't believe air will get into the mouth. The tongue is cutting off the air passage to the mouth. I think why the air gets trapped inside the mouth is, the tongue breaks this seal every so often and air gets in there. And more air pressure that builds up, it causes chipmunk cheeks, etc.
Like the poster above said, you should be able to push that air back, but should seal the mouth from air with the tongue after.
I incorrectly thought that the air actually comes through from the side of the tongue through the cheeks area, but that seems to be false. Based on how this works, that's not possible.
So, tape really doesn't work for me. Tape is necessary if you tend to open the mouth, but I don't. The pressure from the trapped air inside the mouth sometimes force the lips open to let air out. In order to prevent this, the tongue method seems to be the well known trick that works.
Now I can get some REM sleep.