I have a 155 Shikari with the transfer bar system, sn "AU" which would be 1980 manufacture.
Also have a 158 Topper .30-30 pre-transfer bar, sn "AH" (circa 1971).
The ORIGINAL H&R company implemented the transfer bar ("striker assy.") system sometime a year or two before it went under, due to lawsuits from accidents which occured from misuse of the old system and, reportedly, the push-in breechplug on Huntsman Muzzleloaders... the old company also replaced the latter system with a screw-in type breechplug (year unknown) before it's demise, but was unable to continue operating nonetheless.
So the newer transfer-bar set up went into production no later than 1980.
P.S: I just checked my push-in breechplug .58 Huntsman... it bears a sn prefix of AM (1974)
As I believe the legal troubles which doomed the original company to bankruptcy resulted from accidents involving both of the features mentioned, it would seem safe to assume that alterations were made to both systems in the same period of time.
ERGO it seems likely that the start date for incorporating the transfer-bar was between '75-'80.
Steve