How will you make the league something people like?
I'd ask them. I agree that the rules aren't bad, but they aren't very good for the state that the league is in. What I would do you ask them what they would want and do that. Then if things start getting abused, I'd add some rules back and such.
How will you keep the league afloat when the only problem with it is the lack of members?
I think the first thing that has to be done is keeping the current members happy. If the current members aren't very happy, why would anyone else join? I don't know what exactly happened to get this league to the point where people who have PS4s don't want to join, but it's something that happened. If the current members are happy, maybe that'd result in the other people who didn't want to join before want to join.
People might not like Frosty being in charge
Speaking about morale again, but I don't think this is helping the league in its current state either.
How will you get more people interested in the league?
I'd try to talk to Solidus or someone and try to get help promoting that the league is here and people should join. Maybe like a monthly alert letting people know to get people's attention and maybe even catch new members who don't know the league is here because it's almost buried in sub-forums. I'd almost always be talking about it myself, etc