Compare ratings of players over different leagues
An existing way to do this is to use modified Elo ratings.

Video game servers sometimes use a similar scoring system called Glicko or Glicko-2 which might be better for your purposes.

My understanding is that you want to understand the rating of each player relative to every other player and that each in-league rating is essentially the rating of each player in that league relative to each other player in that league. If this is true then there are two ways I can think of to help you work out the hypothetical rating of player X in league L2 based on their performance in league L1:


Generate global ratings based on one of the methods mentioned above and use them to insert the new player in the right place in the ranking
Calculate am in group rating based on the methodologies described above and then calculate the new players ranking by stimulating the score he/she would accumulate if they played each of the players in L2 that they could be compared to in L1 and achieved the expected outcome (i.e. beat all the players they were ranked better than and were beaten by all the players they were ranked worse than)


You might also be interested to check whether the rank correlation between leagues is strong based on players that are ranked in both leagues.