You could predicate added revenue sharing by demanding a certain percent be spent on raising player salary budgets on the lower spending teams.
Yes, owners might demand a hard cap, but poorer teams already get a lot of money through revenue sharing and in other ways. Right now, much of that goes right into the pockets of the owner, as does much of the revenue for richer teams. You can't blame any owner for wanting to increase profits.
Rich teams would prefer there always be 8-12 teams that will always remain relatively non-competitive, in large part to lower spending on player salaries. It gives the richer teams a greater chance at winning and keeping their fan base happy and watching or attending games.
It's always kind of surprised me how the home team gate is not split 50-50 with the visiting team. That seems fair and would go along way at evening the playing field. Home teams could pocket the concession money. There's an argument to be made that the TV money for each game being split with the visiting team as well.
When teams start making 20 times the money playing in NY vs Oakland, maybe some pressure might be put on teams like Oakland to do something, even it that meant moving to a better market area.