To be honest, I wouldn't consider that situation to be viable for adding a storm door. It's a crappy setup to begin with, and adding to it will only make things worse.
There are very good PVC glues available that would work fine for adding the padding I suggested, but as you say, that would make the doorknob situation even worse than it already is. The existing doorway is only marginally acceptable IMO (rental property?), and I wouldn't be comfortable with compounding that injury. Personally, I'd walk away from it unless I was very, very hungry.