update - I got a rovner L13 ligature, and it's too small to fit onto this mouthpiece...unscrewing the ligature to open it to the widest opening, and just barely slides onto the mouthpiece, with no room to fit the reed....
I'll try the suggestion of going to a music store, but that's a 60 mile trek for me, but probably the best strategy at this point in the search..
I'm still curious as to exactly which model Runyon mouthpiece this might be....the only markings on it ar "Runyon" and the number "8"