Poison damage persists through Behemoth's special attack that gives you invincibility.
Poison damage also persists after completing a stage. I died from poison right after I killed Cancer and lost the stage.
Try this: get max boost to either side, make your way up a fair distance, then turn and max out your speed to that one side. My hog has been going for almost 30 minutes, and has climbed higher than when I started on its own.