a good picture of the base would be useful Neil. Sorry can't really help I don't think - I've just looked again at John A. Brooks 'Glass Tumblers 1700 - 1900', and there's nothing quite like your example. Head on block time, but it does seem that the vast majority of C19 tumblers lean towards being conical/slightly conical in shape i.e. narrower at the base, although I appreciate they can also be waisted, barrel shaped (earlier examples probably), or cylindrical. Maybe Continental examples were different. I won't go into descriptions here, because I have to reply elsewhere on a similar subject. What convinces you that yours is a tumbler?
Is jp saying that his C19 Baccarat examples are cylindrical or tapered?