Out of curiosity though, since I didn't note down how many ranked rounds I had completed when I went from TM to L, is there any way I can find out how many ranked rounds I still have left to complete before I reach saturation?
It's not written down in the game, thus for curious minds it may be wise to note the "ranked rounds" number in their profile stats when tiering up to Tour Master, Legend and TL.
But there are a few options:
Most simple would be to wait for saturation, happily playing ranked rounds on courses of Par 60 - Par 80. You'd recognize it by a sudden severe tumbling of your average, even on mediocre rounds, even on rounds above the average. This is due to the highest rounds being kicked out of the calculation and lasts for a while, until the differences between highest and new scores shrink.
Furtheron you might take an intelligent guess. How many rounds do you play in average, per week? How long, how many weeks have you been Legend? Multiply the numbers for a rough estimation.
Third option includes some maths, and it works only for an unsaturated average (less than 500 Legend rounds)!
First, make notes of a series of 5? (10?) ranked strokeplay games that you play: Write down the date, the course's name, your average before AND after and the score played (plain strokes!) It helps to have some extreme scores, 5 shots below or 5 shots above your average. 9 hole rounds are o.k. (double the scores).
Second, check in your score history that you didn't forget any games, and cross out all Par3 and Par5 games.
Then, create a spreadsheet table to calculate the evolving average in cascading the games you wrote down and using a variable as the initial number of games in the denominator. Compare the calculated outcome with the numbers you wrote down (observe rounding differences!).
You should end up with a very good guess!