So, confirmation that hiring them makes them a four person hero ball, but also. That's unquestionably going to be a Heart check, probably contested, but would be much harder than getting favors out of them. Conquering Storm will also help with the check. Their help on the Rudies will not fulfill Canaan's drive either, which would be a problem.
So, what I'm proposing is this
[X] You owe me a favor. (Quartet do an action for Eggman)
-[X] Bring In Others (The Restoration)
--[X] If they refuse, let them go.
-[X] "when you see that blue menace again tell him we're even for starfall islands now and not to expect anything else"
Relatively low DC, they should do well on that. It has threefold, possibly fourfold benefits. This makes the Restoration aware that Eggman saved them, makes the Restoration more outwardly focused than focused on us (especially if they inform the Restoration of other Kings like they are with us), and gives us an additional alliance against the Black Arms. A potential fourth benefit is that this may help counteract the False Flag attacks somewhat.
EDIT: Adding in cjdavis's own addition, fun flavor.