Gotta have the brass tag the SCCA issued & attached to the cage back in the day and the log book, as well as some proof, to run with the group that Ken Epsman runs. When Epsman took over from the previous guy he also tightened up the period-authentic deal, which is why he had the Jerry Schwartz bodywork cut off the Penske/Woods '69 Camaro.
At various times Epsman's owned many of the most significant cars; he's kind of the Bruce Meyer of Vintage TransAm.
Other groups are more lenient from what I hear.