With the frame you have the easy bit done.
Not an oil port for the bottom bracket, but a grease nipple
https://www.ebay.co.uk/itm/ORIGINAL-...oAAOSwUcteIKkx
and get one for the head tube as well.
My standard reference book for the period is the
1952 Brown Brothers catalogue, which should be checked against the
1954 Holdsworth Aids catalogue for any later components
Other Bates owners can be found at this Facebook group
Bates Cantiflex Diadrant Classic Bicycles
Why do you say "semi-period correct build"? Why not full period components?