just a few thoughts which might, or might not, be of interest Otis. Cutting on the upper half of the vase appears to be 'hobnail' pattern (can be either six or eight sided, apparently), quite common in Europe and to a lesser extent the States. Can be see often on whiskey decanters from mid C19 to quite some way into C20 - Davidson very successfully made a bob or two from a pressed version which they Registered.
The lower half is a bit confusing, and looks almost as like Regency slice cutting, although it's not.
The notched rim and the series of small notches towards the base incline me to think it's not British - possibly Continental or States, and maybe from the first 30 - 40 years of the C20, and is undoubtedly hand made, which gives the irregular effect to the cutting. Vases can pick up a lot of wear in a fairly short time, but I think this is a little oder than recent.
How sharp is the cutting? If made before the 1930's it should feel quite sharp - prior to the use of acid for polishing cut glass, and if early you may not find a makers acid backstamp.