Adding a vent (assuming what's there is properly vented in the first place) does not speed up a draining line...so, that's not going to help. Having improper venting (as long as there is at least some) means that the waste will often flow so well that it literally sucks other traps dry as the waste passes by in the main. If I had to guess, I'd guess your main line does not have the proper slope, or has a belly in it. It is fairly common in a drainage system for the waste to only move part of the way to the tank with the first flush. Subsequent water usage will push it further. If there's a bad joint that catches things, over time that may also create a stoppage. Water jetting can clean the inside of the pipe, but it may not always fix something that might be caught in there like maybe a pen, pencil, hairpin, toy, etc., that is catching things. A properly sized snake might be called for. If you can see the drain line from say the basement, check that it doesn't have any dips or bellies and verify the slope (should be at least 1/4" per foot).