"I ended up using EPCOS formers in the end - a lot more expensive than sewing machine bobbins, but at least you can find data on them - there are a fair range of different types - something like an RM7 or RM8 or one of the EP may suit your requirements (The RM8 former does fit over the 6300 ferrite but is a bit loose, so coupling isnt great - theres about 1mm gap.. I think its got an 8.6mm ID.. An RM7 might be a tight fit) - these RM formers are in the order of £1 and available from many manufacturers and suppliers in all sorts of configurations," - FredM
Thanks! You are the go-to guy for weird Theremin magnetics Fred! I could spend (and have in the past spent) all week on the web only come up empty.
The RM7 (B65820) looks really good. As does the B65652BT1, which is 25 cents each (quantity 10 at digikey).
It's no wonder the sewing industry has so much confusion when it comes to bobbins, with no detailed published specs anywhere (that I can find, though I'm sure they exist somewhere if only for manufacture).