My solution was to make the heroes a "branch" of the Freedom League. They're supposed to be able to do the job of the Freedom League in the Midwest. If they call on the League for help all of the time, then they can expect to lose their membership.
"We wanted you guys to help US"
Now, I have no problem with them contacting the League for information, and occasionally Daedalus provides the team with "plot devices" (like an undersea explorer, or space ship). But once they start routinely asking for assistance in a mission, they can expect their membership to vanish.
There's also the issue that the local paper has already expressed doubts about the "junior" Freedom League, especially since all of my PCs are either very young, or are social misfits (mutants, elongating Walrus men, po' white trash, sentient robots, that sort of thing), so the team feels the need to prove themselves worthy of the name "Freedom League," even if it is followed with "Central."








