PVC screen doors tend to sag and warp pretty badly. In addition, I don't know how you would install one without a solid place for the hinges. I understand your problem, but I also understand physics.

 

Call David Copperfield and ask if he has a magic wand you could borrow.

 

I haven’t thought of a way to accomplish what you want to do. My only suggestion is to look at a retractable screen door that you would leave in place but retracted when not in use.

 

look at a retractable screen door

Still have to fasten it with pixie dust an unicorn pee. NO fasteners.

 

By hook or by crook, I’m going to find a way. 🧙

 

Good luck with that. The fancy new aluminum skin covers solid structure, which is what the hinges and latch plate (and closer if it has one) need to be attached to. I've never seen a tensioning type door and not sure I'd trust one anyway. Done properly, and holes you make will be covered by something.

 

Let us know, 'cause we can probably patent it for you.

 

Glue & screw some rubber weatherstripping to screen door frame, then push screen door into frame. Maybe use some rubber cement to help hold it in (it'll peel off)

 

Post a pic of the door and frame.

 

Doors have hinges. I have used the velco and magnetic screens and I like them. not a traditional door, but they work.

 

I have used the velco and magnetic screens

You actually adhered velcro to a door jamb and it held up a screen door? OP is concerned with putting screws into his new metal coil facing. His question is how to get around that.