Just adding "Merry Medallions" (exchangeable for some amount of Siege Sacks or Cosmic Coins, and perhaps also for saving up for a Merry Melee battleground) each tier would add a lot. Also, why limit win rewards to a sleeve? Let's add some exclusive, thematically-appropriate AAs for those who spend a lot of time on a particular mode.
As is, this "You need 4* wins in 5 matches to get any prizes" structure is pretty blah.. especially with the 100p buy-in. Right now the only appeal the mode has is "I like this particular playstyle bunches" and "Pretty sleeve!". There should be some more generalized reward appeal, as well. Some better consideration to balancing before launching a new MM mode would be nice, as well. If manpower is an issue, they should utilize their dedicated fanbase- we'd be able to quickly point out more obvious issues like Frost Wizard in Corinth no problem.
(*Unfortunately, a random rare does not feel like a suitable prize for 3/5 wins. :P)
Improving the MM framework is less obvious and more subjective than in how the devs should address all the other half-completed elements in the game but, either way, it definitely could do with some tweaks moving forward.
A really cool approach, I think, is if they layer it-
Have both a gold version, and a plat version, with different rewards, but shared match-ups on the competition.
As the reward structure is now, though, even gold buy-in doesn't sound all that appealing, especially under the consideration of reduced rewards.
Tying the new currencies together (and mitigating the mess that is Siege rewards) would be good, I think.