The makers' mark is a representation of one registered at the London Assay Office by Thomas Wallis II and Jonathan Hayne in 1810. Arthur G Grimwade, the authority on the matter, reproduced that mark at item 2978 of his book showing a pellet between T and W but also noted that another similar but smaller mark was registered at the same time. Whether this smaller mark carried the pellet isn't mentioned.
A charitable view of the date letter might suggest the items were assayed in London in 1810-11 but the outline shape of the mark is not quite right (the Forum British Hallmarks section provides comparison) and, at best, the Town Mark is an artist's impression of what a crowned leopard's head might look like and is incorrect as is the monarch's head in the Duty Mark.
The engraved words "Whiskey" and "Rye" appear original and indicate an English speaking market.
In the UK there is a distinction between whiskey with an "e" and one without, the former identifying a spirit of Ireland origin, the latter Scotland. A "Whiskey" ticket in the UK would be for the less popular Irish variety and therefore rarer.
I find rye whiskey described on the internet as a product of the USA, rye whisky coming from Canada.
No doubt some residents of the UK would have acquired a taste for rye (whiskey or whisky) but UK tickets for "Rye" would again be rare.
Ruling out the idea that the tickets originated in the UK, the pairing of whiskey (with an "e") with rye, leads me to the impression that the tickets were probably made in and for the USA market but by whom, as you know, will depend on someone having very similar items with a knowledge of their provenance.