And here's the list of the most points scored in a final four game. The most points scored against that year' national champion was Utah's Jerry Chambers with 38 against UTEP in 1966.
So, the player would have to have scored between 47 and 59 during the regular season and up to the Elite Eight. I'll keep looking because I'm weird and I think this is fun, but there aren't really exhaustive records for every game played in seasons 50 years ago, so I'm not sure if I can.