Simulation generated by Cartes-du-Ciel.
Upper path corresponds to the view from Sydney Australia.
Lower path corresopnds to the view from Anchorage Alaska.
The seven path-defining "images" are one hour apart.
Even if the observers of centuries past had not been bedeviled by the "black-drop" effect, the difference in transit timings would have been quite small.
Perhaps those astronomers expected Venus to be significantly closer than it actually is and therefore that this experiment would be easier.
It's hard! Even today, it's less than trivial. It's much easier to measure the
astronomical unit using asteroidal parallax
(see, e.g., http://orfe.princeton.edu/~rvdb/tex/MeasureAU/ms.pdf ).
Below is shown the 1st, 2nd, 3rd, and 4th contacts.
The transit time for the Australian view is 5h 36m.
The transit time for the Alaskan view is 5h 51m.
The difference in these transit times is just 15 minutes.
Converting this difference into a measure of the distance to Venus is more complicated than one might first think. There are several factors that complicate the analysis: