Both examples you linked to have the shorter title.
You mentioned above, when I asked, that yours has the extended/longer title. Hopefully, that's more clear.
In a nutshell: what is the title under the image of your copy?
Is it:
"THE DRUNKARD'S PROGRESS"
or
"THE DRUNKARDS PROGRESS / FROM THE FIRST GLASS TO THE GRAVE"
If your copy has the longer title, its the later reproduction.
And Im no expert, but I also love early lithos, steel cut lithography, hand tinted lithos, etc and have a number of those here, that I have picked up over the years. And when I have, Ive done research to determine what something has been, if I wasnt sure.
Thats what I did with your example. I just love the "sherlocking" aspect of the hobby, too. And learning about when a piece is from, how made, artist, if later repros were ever produced etc.