Only tip I can give is to move slowly, carefully, and tag all those wires that you remove. Most should have a tag, but make backups as the originals are brittle. I think you will have to remove the wires and relay holders from the upper tray and pull the box depending on which area you are trying to access. If you are going to reweld the mount, make sure you aren't melting those wires either!
I only had to pull the top tray for my project so I couldn't help you with pulling the lower box. The only thing I can think of that would be a problem is the relay bases. Getting those past the loom holes might present a problem. I can't remember if the back of the lower box is open to the firewall or not but if it is there will be no problem.
Good luck!

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1983 Mercedes 300SD
1987 Mercedes 300SDL
2001 VW Passat 2.8 AWD
2007 OM642 Jeep WK 4x4