"Mechanicus Reborn" always overwrites the default character, while the character mods listed here will overwrite the default character only if no character selector mod (like miniMAXIme) is active.
Mechanicus (Rebuild) is compatible with my mod. Until it is updated for Factorio 2.1, you can get it to work by changing line 7 of its file info.json from
"factorio_version": "2.0",
to
"factorio_version": "2.1",
Just unpack the mod and edit the file in a text editor of your choice. On starting Factorio, the unpacked version will be preferred over the zipped version, so you don't have to zip the mod again.