Having paid an arm and a leg for a Crawford Truegrip chuck on an L0 back plate I found it was not L0 but smaller

I assume the L00, unless there are any other similar nose fittings out there. Can someone confirm which lathe takes an L00 back plate.
I also seem to have a 5C adapter which is an odd sized taper. It looks like a morse taper but is neither an MT5 or 4 it lies somewhere in between (MT 5 adapter long side in the photo). I think there might be a draw bar kicking around for that but it was too short to go through the headstock on my Master

I assume that it goes on the same lathe.
So before I stick them on John S's site what are they worth.... That L0 backplate I needed was not cheap

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Jo