As Scott said you need to basically get your AVG down to 59.999999.
Pardon me, but your quote and your number are both imprecise. He stated "60.000", and that is correct. It's sufficient to hit that number.
There is a way to calculate exactly how many scores you still need to Tier up but someone else will need to comment on that as I don't know that.
That would be difficult unless you know all the past scores.
It's easier to determine how many rounds are missing to saturation, before the fact.
BTW: I saturated as a Legend close to 2,000 rounds...
For the OP @61.88 average, it can be said that a saturated score pool would encompass 61.88 x 500 = 30,940 strokes while a 60.000 ave. equals to 30,000 strokes. So, he needs to shave off quite a few strokes by eliminating higher scores from the pool and adding lower scores around 60. To say that he's close would be quite an exaggeration...
My 2 Pfennig for the OP: Play the game without caring much, put your fun up front! The "numbers game" is quite a grind, exhausting if you concentrate on that!