I wouldn't bother with a authentic restoration, maybe if you can come across some late stamped unmarked or byf parts I would put a preference to using those, but below are the general type of parts you would need to follow to restore a byf/44 c-block:
Bands - Stamped or solid milled, would have last four digits. Milled band springs are most common. (RB's are almost always milled until the g-block)
Trigger guard - stamped TG and FP in almost all cases, TG last four and FP last two digits. TG two e/135's. When milled FP no waffenamt, but four digit serialing.
Bolts - all recorded are FN (e/140), last four on all parts, last two on ebox.
Stocks - all known laminate, but walnut is known a-b blocks. buttplates are often sub-contracted. Typical E/WaA135 RS, wrist and probably lower butt, though the latter is rarely clear or defined.
Naturally, such a restoration is probably impractical to take to extremes, but use the above as a guide line, the forum probably offers examples in pictures, maybe not a c-block but generally up until the L-block things are serialed in one manner or another and milled is possible, though increasingly rare, well though most of 1944.
Might be best to just stick with e/135 components and not worry about serialing or proper component make, maybe focus on keeping consistency in overall condition and appearance.
** I agree outcome will value to the sum of parts used, that is generally true of all restorations, most, if not all get parted out in one form or another. Personally, I wouldn't bother, money involved (if quality parts are sought) could probably buy a decent bolt mismatched rifle in pretty good condition. Really as good as any option is just stocking and outfitting it with rc parts, make it a shooter, would still be an original finished un-dicked with metal b/r and otherwise as "historic" as any rc (which are pure nonsensical propaganda used to inflate their value far beyond any realistic measure... which of course is the purpose of propaganda, promote or inflate a product, cause or ideology... unfortunately this works nearly as well on reasonably intelligent individuals when repeated over and over as the stupid and gullible..)