If your lessons are, or could be, done in a church or other auditorium that has an organ, you might find that the organ plays midi files. Many such do allow the organist to record and play back parts or complete performances, and and will play any midi you have recorded on the appriate medium. Some have very complete "voicing" that can replicate as other instruments, although some only have "common organ voicings."

Some organists I've known have used the feature to play "duets with themselves" by recording the "hard parts" in practice so they can make corrections and adding the fun part in the performance. (It's only "cheating" if someone finds out you're doing it?)

I haven't seen much on this feature recently, and older organs generally used "floppy disks" for the recording that may be a little hard to find, but the connected sound systems might minimize the need to haul other equipment in and out for training sessions.

It would be advisable that you speak to the organist before playing with their "personal toy" since some have "proprietary feelings" on the subject; but if the equipment is there they shouldn't object to it being used, and might be willing to offer help with it.

John