Here are couple of suggestions.
How about alliance based tournaments?
The winners list would be based on cumulative points from all alliance members and alliances members who opted for the tournament would get rewards.
Then, there could be not-blind tournaments , where you know who is your opponent from the start. Or is there a fear that people might use that for cheating?
Also, knock-out style tournaments might be fun, where winner proceeds to the next stage, until the final.
Alliance V Alliance would HEAVILY favor just a couple of stacked groups (no offense) but if they presented it more as a total number of battles = number of points, that would be more fair.
1 - 5 battles = 500 pts
5 - 10 = 1000 pts
Now of course the more dedicated alliances would also have the most battles, but at least it wouldn’t come down to number of wins, meaning any alliance could in theory have a chance to win.
The knockout idea is also a good one, IMO would be a better way of determining skill VS the person who has the time for the most battles. Have a set period of random battles (maybe Fri and Sat) and then on Sunday take the top 64 (128/256/512, etc) and put them in a bracket. Whoever can go undefeated is the winner.
Or maybe, for alliance tournament, each alliance could send like three champions to represent them
As for the knock-out, I guess the most complicated issue is schedule. It would probably have to be organized by time-zones. So, each player would first opt for the time zone he is in. Then winners by each of 24 timezones could fight in a successive scheduling.