A picture equals a thousand words. All has become clear. Francis Barnett couldn't have used the original Villiers Heavyweight carb on the Cruiser anyway. Like all Villiers carbs it had an integral floatchamber and couldn't be mounted at an angle to be hidden under the Cruiser bodywork as shown in that photo.
It appears Francis Barnett turned to AMAL
for a solution who in turn provided a carb in line with a fad of the day.
For a short period in the late 1930's the British motorcycle factories experimented with mounting AMAL
carbs on their side as shown in the picture. Mainly this was on tall four stroke singles where there wasn't enough room under the tank for the usual vertical mounting. It worked well enough when the carbs were new but quicjkly became frustrating with a little wear leading to much frustration with flooding, slides jamming and of course erratic carburation from odd wear pattterns in the needle jet.. It was not a happy experiment.
Owners always talked of having to take extreme care to get everything just so and to keep it that way. The concept had very few enthusiasts.
Nowadays it is possible to have carb bodies re sleeved with a stainless steel sleeve and I suspect you may have to go down this path as well as fitting a new standard 4/061 needle jet.
Best of luck.