hay sal,
there are 2 ways that , i can think of , one way is to of course take the door off and cut out the rust get a clear piece and weld ( i know you know that) that would be the for sure way to get rid of it.
the 2nd way would be to get some POR-15, not sure if your familiar with it?
if not here ya go
POR15, Inc. - Stop Rust Permanently - Repair Gas & Fuel Tanks they sell a starter kit, which should be enough for what you need, i used it on my car. in your case grab a steel brush so you can knock off as much rust as you can, ( not to hard -you know what i mean , enough to knock off the surface rust ) then you get the marine clean degrease, then spray on the metal ready cleaner liquid it comes with let it dry and then brush on the por-15 . they might have a catalyst
which helps it dry quicker( ask when you order ) anyway the kit goes for $20 bucks, I am an elevator mechanic and we use it on the outdoor escalators
and we have not seen rust on them, i have por everywhere on my car just in case. the por is black so on the underside you can't even tell. I hope this helps, i can say it does work, some say no, but applied the right way worked for me. just prep the rust spot first.