I'm just gonna throw some ideas at you all.
If you're not interested, don't read it
This might sound stupid and I'm sure it's flawed somehow, but for keeping track of battles, why can't each leader just have a separate thread, in which they post those who beat them? (It could all be done in a single thread too, it might be more cluttered that way though) Obviously there's the issue of anonymity with this, but if it's made very clear that only a certain amount of challengers are accepted per day, why would there be problems? I'm sure there'll be one or two people who don't read the rules and spam like crazy for a match, but as Mde said, they could just be banned from the league from breaking the rules.
Here's another idea (Considerably worse)
If people could just post something like "Challenge: 1", "Challenge 2" etc. on the leader's thread, (Each new person typing the next number) along with the date of the challenge being issued, that could replace a more complicated system. (It would probably be quite messy though, plus, if it's popular, people could be ninja'd or something)
As for this being difficult, I reckon some sort of "Tryouts" thing should happen for potential leaders (Providing there are even enough volunteers).
Get maybe 3 "Judges" who are actually good at Showdown,
get the potentials to battle the judges with their monotype team and let the judges decide whether or not they think that person and their team have the required skill/difficulty to be their respective type leader.
As for Usable tiers, I should think it wouldn't be fair for challengers to use full legendary teams,
I don't know if League is always OU or there's some sort of rules regarding this, but if it were up to me,
I would say that challengers should be confined to OU (Including OU clauses, etc.) and maybe the leaders should be allowed one non-legendary Uber (Maybe not, purely for difficulty) and are otherwise restrained to the same OU rules as the challengers.
Anyway, this is all the stuff I thought about today x_________x
Feel free to comment about it