this may be a form of dram glass, but in my opinion is not a firing or ships glass, and from what you say it sounds to be too light in construction - and certainly looks more like a cheap pub/tavern glass from somewhere around the late C19 or even into the C20. I can't see much wear on the foot of this one, and would suggest that the base mark you mention is possibly where the pontil scar has been reheated to remove the sharpness.
The lack of wear, absence of a sharp pontil scar, too small a foot and possibly the lack of a lead glass ring, all contribute to saying this is wrong.
Firing glasses were popular throughout most of the C18 (but don't think they started until c. 1730) and crept on into the Regency period and there are even some known to be dated as late as c. 1850 ish, apparently. Their feet were exceptionally thick - likewise their short stems - with conical and trumpet bowl being possibly the most common, and they're found often with Masonic engraving/decoration. Construction is frequently with a drawn stem.
Ships' glasses are similar apparently, and are said to have even wider feet, for obvious reasons. Both Bickerton and G. Barrington Hughes show examples - although Bicketon is rather short on text.
Believe Peter has a great collection of dram glasses, and we might persuade him to show us some C18 firing, ships' and dram glasses - if he's listening
