15 minutes already sounds very long.
The computation of the MNE inverse solution is independent from the data and is expected to take only a few seconds.
Your signals look very long - is this resting state data?
In general, we recommend importing native file formats instead of manually semi-processed recordings from a .mat file, and then linking them to the database for preprocessing using the menu "Review raw file", as illustrated in the introduction tutorials. But maybe this is not applicable to your case.
https://neuroimage.usc.edu/brainstorm/Tutorials