Sounds like the vent is plugged. When you flush and the mass goes into the tank, the displaced air has to go someplace. That is what the vent does. If the tank is not vented, that air has to come back out of the toilet, hence the burp.
A mound in the tank causes problems, but not THAT problem. It doesn't block the air from escaping the tank on flushing.
Tank flushing systems only have one sprayer in the tank. It either just sprays like a garden hose nozzle set on "shower," or it rotates spraying as it goes around.
My first step would be to go up on the roof and remove the vent cover. Look for visible obstructions, like a wasp nest. Look to see if the vent pipe may have come loose and fallen down into the tank so it is no longer above the high water line. If it falls down where it is below the high water line, it can't vent once the water level covers the bottom of the pipe. Put a water hose down the pipe and flush it out in case something has the pipe blocked at the bottom where you can't see it.
I once had a MH that developed a sewer odor in the bathroom. I traced it to the under-sink AAV (air admittance valve) being bad. I replaced it and it fixed the problem. Until I dumped the tank and it came back. I eventually figured out that the tank vent was plugged, and when I dumped the tank, it broke the under-sink AAV trying to vent the tank. Once I flushed out whatever had the tank vent blocked, and replaced the under-sink AAV AGAIN, it never recurred.
Bobbo and Lin
2017 F-150 XLT 4x4 SuperCab w/Max Tow Package 3.5l EcoBoost V6
2017 Airstream Flying Cloud 23FB