Nicklaus is a bad example War. He focused on the majors and never won the Vardon Trophy for low average because he never played enough rounds in a year to qualify.
The lowest ever average is Tigers in 2000, 67.8, before tournaments started to Tiger Proof their courses.
Gotta say though your numbers off the top of your head are pretty good.
Took a sample of averages by tier this morning using the search, at least 100 players in each tier. I only used on-line players so there are no dead accounts. And to get a bigger sample of Legends I used some offline averages but weeded out any who were still at level 30 indicating they hadn't yet played under the new conditions.
Here's where the averages are today.
.............Warof1812..........Avg............Top 20%...........Top 10%.......Range
Legends........68..............65.4................62.0...................61.1.......57.8 to 74.5
Tour Masters 69..............66.9................63.9..................63.3........62.3 to 77.3
Masters..........70..............69.8................66.9...................66.3.......65.4 to 78.2
Tour Pros.......71..............73.6................70.1..................69.5........68.7 to 82.6
Spread between the top 10% average and overall average
Legends............. -4.3
Tour Masters.... -3.6
Masters............. -3.5
Tour Pros........... -4.1
Someone's likely to ask so...........
What if WGT created a new tier for the top 20% of Legends, cutoff at 63.3. The best of the best, call them the Ultimate Legends. And assuming ULs and Legends are still on the Championship tees.
..........................................Avg...............Top 20%.........Top 10%.....Range
Ultimate Legends..........62.0................60.8.................59.7......57.8 to 63.3
Legends...........................66.2................64.1.................63.7......63.4 to 74.5
Tour Masters..................66.9................63.9.................63.3......62.3 to 77.3
Masters............................69.8................66.9................66.3.......65.4 to 78.2
Tour Pro............................73.6................70.1................69.5......68.7 to 82.6
The spreads between the top 10% average and overall average would be:
Ultimate Legends... -2.3
Legends.................... -2.5
Tour Masters........... -3.6
Masters.................... -3.5
Tour Pros.................. -4.1