Hi Lugerfan,
IMHO the scope has NOT been refinished. I suspect the original blue on the scope tube has simply worn off over the years. The scope is right enough, but looks 'well loved'. The black paint on the turrets is probably original & has just survived better than the blueing.
I don't know of any written source on serial numbers but there are enough people who have seen/owned/handled enough 4T's over the years to have a good idea where number ranges start & finish. Most BSA 4T's date from 1943/44/45 & during 1943 a sequence of two letters (an 'A' followed by a second letter that progressed through the alphabet as the year went on: AA, AB, AC...........AQ, AR, AS etc) & then 4 digits, was used. In fact it continued over into the very beginning of 1944, but was soon replaced by a sequence of 5 figures starting with a '3' & after the first production run that had no prefix, a letter was added at the beginning. eg B 32657, G 31965, R 38902. This system continued until the end of production. It seems that the changeover from 1944 to 45 occurred in the R prefix range as rifles bearing either date can be found. I have not seen any 4T's with letter prefixes after X, although I have seen a 1947 dated No4 in standard trim bearing a Y prefix serial number.
Without getting overly complicated, the vast majority of BSA H&H 4T conversions will have the D6E Enfield examiners mark, but this is often missing on earlier conversions (1943 & before), or may be present in a non-standard place (I own several rifles of 1941 mfr., converted by H&H & which bear this examiner's mark on the knox. Odd, but true).
I have a No4T for sale at the moment, but whilst it is 100% genuine, it is a mis-match, has been refurbished & it is a section 1 firearm.