Both Roy Bacon books....BSA Twin Restoration and BSA Twins and Triples detail cam timing for 334, 356 and 357 cams. Neither publication shows the actual cam lift as far as I can tell.
BSA Service Sheet 701 also lists the cam timing, Sheet 702* gives cam bush finished bore as 0.7485"/0.7495". These bushes are rarely changed on the average clanker, if the cam turns with no binding or tight spots that's good enough for the likes of a cheapskate such as me.. A free running cam is also a quick test for a matched pair of crankcases. Perfection will certainly cost, new bushes, installation, line boring. Fine with your own machine shop, not worth it for leisure riding.
New cams are available from Hepolite, now a Wassell brand, nothing to do with the trusted AE outfit of yesteryear. Newman Cams in Kent are well respected over many years and good to deal with. But in the above listing, I don't know what they mean by A6...Their notation for earlier A7 Longstroke, perhaps.
A reprofiled cam will not have the same heel to toe dimensions as a brand new offering. This is because material is removed from the heel of the cam to restore the original lift. Genuine OEM cams will have the part number stamped on the blind bush end. Choice of standard profiles performing with differing compression ratios well documented already in Forum posts.
Swarfy
* Available in Forum Literature Section, or hard copy reprints...got mine on ebay.