First off - I'm having a blast playing this. I really like the concept of FM meets fantasy and am comfortable with the concept of leagues.
All the normal disclaimers - I don't pretend to be a game developer and I'm sure many suggestions could have unintended consequences elsewhere in the game.
If you wanted to make each season's point climb more immersive or realistic an option could be some variant of changing league points to "honour", "glory" or even "popularity" - same principle different name (but distinct from the existing renown for the guild). The simplest version would (at least to a non-games designer) to multiply the points earned by the delve rating to get a single "honour/glory/popularity" score for each league match. So say 3 (for success) * 90 DR = 270 or 2.70 overall score.
If you chose to complicate this then this could be a way of tying all the different systems together - the bulk of the points would still be earned through the league, but participation in the various wars and for successfully carrying out the tavern quests would give a few additional points. It would give players more incentive to do these side activities and mean they have to balance more the risk / reward of sending adventurers away for tavern quests while maintaining enough strength for the league.
If you wanted to push it even further, then certain traits or equipment could be used to influence the score - a bonus for using a hometown hero in a league, a penalty for a hated or unpopular but powerful monster in the league? Some equipment could give score bonus but with limited other bonus or penalties so balancing best stats with bonus points? (Sponsored equipment that gives gold bonuses if used for a clear but potentially slightly decrease popularity/glory from that run - that might be a little too far?)
On the renaming front, maybe cup could be renamed the Arena series, Gladiator series; something that emphasises the spirit of the activity, with slightly less direct Football Manager language.