Thanks for your comments Phil.
I was checking the frequency on my counter, and only decided out of curiosity to check the waveform - I'm beginning to wish that I hadn't now!
Basically it's the same circuit as the modulator part of the BVWS FM/AM converter. Simplest thing to do will be to change the transistor, more in hope than expectation.
Yes, the Mini Mods that I've built have had a clean unmodulated output as shown in the pic below.
When I work out how to use the FM module I'll report back on how it sounds.