Hi - would agree with you that similarity of your bowl/stem, compared with the same features on the 'Scottish Regency Cordial Glass' is very obvious. Unfortunately, the distinct bucket bowl on the two examples here, both in capacity and shape, and as a dram or a cordial, doesn't appear in Bickerton. The 'Regency' example for sale, is rather vague on date - Regency being generally 1790 - 1830 ...... do you agree?
Bucket shaped bowls appeared on genuine long-stemmed cordials for much of the third quarter of the C18, apparently, but bowl capacity was noticeably smaller than the two being discussed here, and this might suggest that the two here are of a later date - 1830 - 1840 perhaps. And then again we have the issue that you're suggesting yours is a dram, and the other is being sold as a cordial.

My uneducated suggestion would lean more toward a dram than a cordial.
I could be wrong, but comparing feet on these two drams looks to suggest that the one for sale has a noticeably flatter foot than yours - what do you think.
Some shapes from around this time, particular pieces for pub/tavern use, do have much similarity in appearance - bit like some of the common shapes for rummers - just a quickly made utility glass, and made to a standard design. You could be correct insofar as same maker, but it would be impossible to know, and without genuine proof very wrong to say so.
I hate to be a killjoy, but I think the same reasoning applies to your query regarding your comparison of the engraving on your dram, and the ale, as being from the same hand. This heavy squared, u/c serrifed-type-face appearance was commonplace for wheel engraving for much of the C19, and whilst I might be wrong, think this explains how two different glasses - separated by perhaps half a century in manufacture (if that is indeed the case) - have what appears to be wheel engraving 'by the same individual'. IMHO the appearance of the engraving 'hand' on your glass and the ale is nothing more than coincidence - a commonplace style of engraving used over many years, and doesn't suggest the same engraver or an error in dating.
What I think is striking regarding the appearance of the Scottish dwarf ale, is how the shape would pass perfectly for a champers flute - in fact take away the words 'Disher's Ale', and you have a glass that looks more like a flute than an ale glass. Most dwarf ales from this period, and either side as well, don't have this drawn stem feature. But, of course, this one does carry the word ale, so a dwarf ale it has to be

Regret this doesn't really help with dating your glass - but if you look in Bickerton (do you have the book yet?) you'll see the quandary in trying to match your bowl shape either a dram or cordial pre 1830. I don't suggest the flat foot is an issue, it's more the bowl that's a problem.
But then what do I know - where are all the other drinking glass contributors to the forum.

Peter (oldglassman) do you perhaps have a moment to give this one some thought please, or are both glasses outside your period ?