I agree with the challenge of relegation - what should happen to the team?

Just too let the team be relegated could be a too strong team for the lower league. Maybe a check, that players that have higher Q than it's possible to buy in the new league, will loose Q to match the level.
Players that are lower Q than you can buy at the relegated level, could just be the same.

Prize gap seems pretty high, at my level I could earn a lot more from cup than CHL and league.
Total prize earnings for going all the in all competetions are:
CUP: 37,57m
CHL: 17,84m
League: 17,58m

So for prize money, the cup alone can provide more money than league and CHL combined ! So I can't recall the picture you describe, where cup prizes are lower than CHL and League.

For reference, I'm at level 6 (league and CHL) - cup would be guessed to be level 10.