I don't have an awning rod anymore (electric awning) and if I had one it wouldn't get past the two elbows.
I'm not thinking that I have a pyramid.
No, I don't believe that you have a pyramid either.
I had something very similar to yours and the "it wouldn't get past the two elbows" is what I think is the problem.
When you flush the water flows but the "heavier stuff" goes to the bottom. There are no currents or movement of liquids to move stuff around. Soon the heavier stuff and paper start up the pipe creating the almost perfect damn. This takes a day or two to start. The burp when you flush is air caught between the water starting down and the "dam" below. Take a "snake" or whatever is handy and move it around a bit and see if the burp disappears for a day or two. Usually, the more the toilet it used, the more the burp tends to disappear, from the higher fluid level in the tank.
I've read many times on these forums to test toiler paper, drop a sheet in a quart of water and see what happens. Doesn't matter, no one uses it like that. Wrap ten sheets around your hand, drop it in, and see what happens. That is how it is used.
I won't mention what one of my former jobs was but think Mike Rowe.