Those door side moldings would be more work than its worth to remove and reinstall on your project IMHO. Double face taped just like the lower door moldings which are yes, just like wet cardboard. In my experience, any cracks or tears will open right back up during installation when pressed on. Repairing it on the car is arguably a better approach depending on the damage. The type of plastic its made of is not great for repairing. I believe GM intended them for one time usage, and outdoor exposure and age has pretty much ruined them all by now.
The freak show that happened with the paint was from applying it too wet. The solvent in it penetrated the primer and featheredged existing finish, and swelled and lifted wherever theres an edge. Catalyzed products don't do that as bad but its a big issue with air dry products. Spray super-light for the first couple or three coats and let each coat flash dry for a lot longer. You can dump enough on with the later coats to smooth out the dry coats but you still gotta keep it like medium wet not full wet when the substrate is as sensitive to solvent as yours. If its cold in your paint spot... thats killing the paint working like it should. Stays wet too long and causes what you're seeing, solvent penetration. Paint can't dry right under about 60 degrees. Thats air temp but just as importantly the temperature of the part being sprayed.
Curious if you followed instructions on the mesh tape and epoxy because normally for a repair of that nature a bed of repair material is applied first over an adhesion promoter coat, then the mesh is pressed into that and then buried in another layer of the goop. In any case, on the face of the part, your filler should extend well beyond the repair area.
Soooo yeah you have work to do. Study hard and stay with it!