allon wrote:You don't want to solder that.
Weld, maybe. Either way, you can't weld/solder to rust.

You might break apart the ceramic to try to get to uncorroded metal, and then build up a new insulator.

Is that the high current coil or the low current coil?

The broken off post is not rusted. The picture makes it look that way, but actually it's shiny metal there.

How about soldering in place, then covering with epoxy, essentially embedding the whole connection. Is that crazy?

A quick reply. Fuses are a good thing and cheap. Replace the fuse.

Some more thoughts:

If there's a way you can make a firm physical connection that solder would only support, that would be good. And maybe there's a high temperature solder. Someone in a local appliance repair shop might recommend a good product. I like your approach of sealing it in with epoxy, which is what I did.

For removing that bar to check the heating element resistance, how about soaking it in penetrating oil and being very gentle in freeing that up? Then clean that off of course.

For the rust, polishing or cleaning it off and applying high temperature rust oleum can preserve your base as long as you make sure no more water is getting in.