If you need to wiggle the relays, you may just need to replace the terminals:
https://www.delcity.net/store/Female-Terminals/p_9291.h_150481

Often, the terminals get corroded or loose from use, both conditions can overheat the terminals without blowing fuses, that causes the melting.

Easy to switch or add circuits. I've added a extra circuits (relays and fuses) in many of those boxes. The hardest part was finding a source that didn't have a 1000 part minimum order....
They make a tool to remove them, but I just use a ground down nail file or small screwdriver to press the keeper tab in from the top.

You can pick up the plastic cover they fit in (on the one I have it's yellow) from a scrap yard for a few cents, they're just held in with push tabs so you can pop them out with a small screwdriver. Or just move the relay(s) to one of the empty spots.
Much easier and quicker than replacing the whole thing.

 

Thanks Maxtor, never thought of that I will explore that option