Hmm...you know I have to say that I've honestly only ever had 1 Atari carts go bad that I have during all my years now.
1 was a copy of F-14 Tomcat for the 7800 that just suddenly died and wouldn't work anymore after the first week I got it. I exchanged it for F-18 Hornet instead at the time.
the 2nd game is a copy of Tapper for the 2600s. I've taken the PCB out of the shell and scrubbed and scrubbed it to no avail. I even checked continuity on the contacts to as close as I could next to the blob hiding the actual ROM and they all checked good. So no ideas on that one. But I've also got like 3 or 4 games that are literally just laying around and are nothing but the bare PCB and I've them for well over 20 years like this and they still fire up to this day?!
I guess my point is that I would be surprised if the carts were actually bad and might not just need more vigorous cleaning on them? Using a pencil eraser on the contacts works well. Just use some alcohol and q-tip after to remove the eraser residue.
Or..it could be due to the BIOS in your 5200s still being 2port versions and the reason the ones on your flashcart work is because they are already modified versions of the roms that will work on standard 2port 5200s.