Re-referencing the active electrodes

Keep the type of the EXG* channels as "EMG".
For display purposes, do not use the process "Re-reference EEG". Instead, create a re-referencing montage that you can edit freely and include, as I suggested previously:
https://neuroimage.usc.edu/brainstorm/Tutorials/MontageEditor

If you want the re-referencing to be used for further analysis steps that are not linear (ie. other than averaging, filtering, source estimation), use the process "Re-reference EEG" but only for the EEG.

For saving permanently the re-referenced values (ie. if you want to export the recordings outside of Brainstorm) or if you need to process the EMG signals, you could use the process "Standardize > Apply montage" with the montage you created previously for display.