I certainly agree with your diagnosis that the vent pipe is clogged. Unfortunately I don't know of any way to clear this from below unless you are able to locate and cut into the vent pipe (probably in the wall behind toilet). Clean-outs are always directed to follow the flow of water (downwards), so it is difficult to clean up the vent. Hopefully the reason the downstairs toilet is affected is a clog in the pipe above the upstairs toilet, and the downstairs toilet is re-vented above the upstairs unit, otherwise there should be 2-stacks.
The vent should emerge from the roof at about 18". In very hot climates, the ABS pipe can sometimes actually melt or deteriorate to close off the opening. Most of the time, a critter has crawled or flown inside attracted to the warmth. Sometimes, a 1-way trip.
The clog should be fairly easy to clear with a conventional snake, but since the roof is high and steep, you may want to hire the job to be done.