What BJF pedal would make a good stack mate for the EGDM? I was thinking along the lines of something that would provide a nice boost for the EGDM for leads, but at the same time something that would sound great on its own into a Fender Deluxe. LGW, RRB, BBOD?

The Red Rooster would probably be a good choice to enhance to qualities already present in the EGDM. I think an RC Booster could be a good choice too.
A good treble booster might do it too.

All good choices, but they do different things... the RRB is a natural boost for the EGDM and sounds amazing clean with a Tele into a DRev...
The LGW is also a good boost as it has low compression so it could push the EGD into some comp of its own without overpowering it....
and the BBOD is excellent with a DRev for lower grit playing or higher drive/distortion....
just depends on what you want...