Hi there, Ian,
Just a suggestion but might the oiler hole tappings be BSP?
Regarding the back-plate being 3/8" Uni, is it the chuck body or the back-plate whose holes are tapped? Remembering that Whitworth threads are 55 degrees and Uni threads are 60 degrees, I think it unlikely that the chuck body tappings would be a mixture of BSW/BSF and Uni. (From memory, some sizes of Whit and Uni share the same TPI.)