Based on a YouTube video that I came across, I knew once my screen door latched broke, I was going to do this mod.
Here's some pictures on my setup. A local tool store had some magnets that I picked up.
The larger one used on the main door were about 0.5" dia x 0.25" (8lb) and the ones I used on the screen door were 3/8" dia x ~1/8". I used some Gorilla Epoxy Glue that I had and took a couple days to epoxy one side, then the other, etc... Also epoxy some washer to provide a ferrous surface for the magnets to be attracted to. I used 3 small magnets on the screen door, could get by with less if you want. Think you need at least the 2 of the 8lb magnets to hold the door to the screen frame so it doesn't come loose when you open with you a quick tug. Maybe you can find one 16 lb magnet instead of 2...Anyways, this is my setup. We'll see how it works on our next trip. Handle is a Camco handle.
5lb Magnets: General No. 342 ($6, 5 pack, Local Supply)
8lb Magnets: Enkay 4480-C ($8, 4 pack, Local Supply)
Camco 42183 Door Handle (Amazon)