I can see you've never tried to weld rust

Don't waste your time.
You must either remove the rust or stop it from spreading. Period.
Overlapping panels are rust's best friend because I don't know of any product that can get in there and stop it. Eastwood sells their
RUST CONVERTER in an aerosol and it's as thin as brake cleaner. They claim it can seep into seams so it may be your only non-surgical option. I've used it and feel that it does an excellent job but time is the test and I've only used it within the last year so I can't vouch for it's long term effectiveness.
Have you had a look at both sides of the area? A BB-sized hole on the outside usually means a square foot of rusted area on the inside.