Impossible to drive that far on no oil!!
It is possible for a 1968 Mustang with an engine in poor condition to lose 4 quarts of oil in 300 miles. one or more stuck or broken oil control rings, malfunctioning PCV system, excessive internal engine wear can all make this happen. This is especially true if the car was driven hard for 300 miles after sitting around for a long time.
This vehicle, 40 years old, must have sat often unused for lengthy periods of time and has no doubt deteriorated seals. On a fast highway trip oil can disappear in the various ways mentioned, without leaving signs of leakage or visible blue smoke in the exhaust.