Flipping BioSemi EEG layout

You must uncheck the option "Apply voxel=>subject transformation from the MRI".
I've tried importing the file you posted on the ICBM152 template, and it works...

Since you made it a new template, you can also select it in the line "Or use default", instead of selecting the .mat file.

Additionally, if I take the grand average of the participants (consisting of both flipped and un-flipped EEG positions from the method described above) the resulting EEG positions become something like this (shown below). I imagine this is because Brainstorm is trying to take the average point of flipped and unflipped EEG positions and take the middle point between the two (because the Flipped electrode positions are due to due EEG Position channel files).

Indeed, it indicates that your channel files do not match across subjects.
You need to flip the rows in the ERP data file and THEN replace the flipped channel file with the original channel file.