I wouldn't go near it with a soldering iron. It might be fine, but I wouldn't do it. As I understand it, you'd need a BIG soldering iron (like they use for stained glass work, not for electronics) and even so you're not going to get the frame hot enough for any kind of solder to stick well enough. But, I emphasize: what do I know!

My thinking is: if you dissolve away all the rust, you'll be left with a porous surface to which the epoxy will stick just fine. The fix will not be "good as new," but if done right you can have something that works and looks okay without any further compromise to the originality of the frame.