Hi Sparrow,
Best medieval music group "Early Music Quartet" a.k.a. "Studio Frue Musik" - Bernard de Ventadorn/Matrim Codax and Carmina Burana albums are fantastic.
No one know what medieval music performance was like as Edison had not been born early enough.
Hildegard von Bingen is a lot more interesting than plainchant.
You basically have your imagination and the older folk traditions as done by Musica Reservata, and Binkley's group.
You do not need to use vibrato to play the theremin, but TREMOLO . . . let's don't go there.
I started out doing medieval electronics, I am a purist!
https://www.soundclick.com/bands3/default.cfm?bandID=646320
As for the theremin I have "Ecce Gratum" C.B.143 done in a planetarium with Art Harrison in a very non traditional arrangement:
https://youtu.be/wtDwqGQtsvg
(there are no traditional arrangements)
That was a long time ago. Back then I still over-did vibrato as I was still a novice.
I did some "electrograss" and that styling is more likely to be adaptable to medieval works:
https://www.youtube.com/results?search_query=%22rupert+Chappelle%22+electrograss
But as to what I do now, I would recommend the Mel9 for your theremin. You can add vibrato when you like, but I advise to first hit the note and hold it, then express.
https://www.youtube.com/results?search_query=%22rupert+Chappelle%22+%22national+electrophonic%22
Not only can you play with or without vibrato, but you can play staccato as well. Avoid pizzicato - that ruined me for a year.
A group doing medieval and renaissance music in performance electronically would be a delight.
BTW- If hillbillies can sing on pitch, I suspect troubadours could as well, except for that famously bad one.
https://youtu.be/T8gat9iwqMM