A large sheet of charcoal or black paper from stationery shop makes a serviceable background. Try oblique lighting rather than full glare which will only bounce of the glass and destroy the contrast.
Assume no markings at all.......... of course, always the possibility this might be Georgian - i.e. C18/early C19 - but the likelihood is small bearing in mind the survival rate of glass that is two hundred years old, or more, when compared to the volume produced since - with more recent material having a progressively higher survival rate the nearer you it approaches the present time.
You say this is a head scratcher - are you suggesting you have searched the literature exhaustively without success, or perhaps just the internet.
As you can appreciate, there have been vast amounts of cut glass produced in the world, over the past 100 years alone, and unlike a lot of pressed material it's less easy to find attributions/provenance, especially in the absence of a backstamp.
There are factors that might help to narrow down period and country, possibly ............. colour, wear, sound when flicked, sharpness of cutting etc., but your description so far is inadequate to make any headway.
Wait to hear from you