The location is a fictitious island at 30ºS, 19ºW.
I believe that with clear skies the transit would already have been visible at sunrise; would this have given any odd effects, for instance caused by the extra thickness of the atmosphere at the angle they're viewing at?
What time would the transit have ended?
What equipment would they have used to project the images onto a screen?
Calculations: what would the parallax calculations look like – and also calculations for establishing longitude, eg lunars, Jovian moons (if relevant; I am on a learning curve so steep it's more of a cliff.)
Andrea Wulf, Chasing Venus
Royal Society: https://royalsociety.org/exhibitions/transit-venus/
Museum of the History of Science: http://www.mhs.ox.ac.uk/venus/
I've found plenty of pages on the 1761 transit, and more recent ones, including the one I saw in 2012 – but honestly it would be lovely to have one definitive place to go.