T i m wrote:

I tried putting it in the lathe earlier but it's just too unstable to
be reliable (and I've images of it flying across the workshop, never
to be seen again) :-(

The trick for machining rubber is to cool it down to about -50 deg C
first (then work quickly). I've seen this done and it's very effective,
but the trouble is that a small workpiece like yours will probably warm
up too quickly for the technique to be useful.

Freezer spray or a Peltier cooler module from RS will get you down to
somewhere near the target temperature.

--
Andy