Apparently I'm being dense, thank you.
The threads on the LU60 adaptor match the body threads on a P/C/etc. With the M2 head being so much chunkier it had not occured to my to try it...
A C2M stacked onto an LU60 will do what I'm looking for.
It definitely isn't a C-M (unless I combine that with another adaptor?) The body has internal threads, not external like a P/C/etc.
For reference, this LU10 adaptor has the correct threads for the head and body but also lengthens the light to 3-cell.
What I need is something like this LU60...
I have the light in the picture below which has, I believe, an M2 head (there's a P60 lamp in there).
In one of those deals where you acquire a bunch of random bits I have acquired the head pictured which is from an M962 (it has the shock absorbing reflector and takes the MN10/11 lamps) and an...