You know what's interesting everybody in the Restoration, and possible GUN, think Eggman is gone and would never return. I imagine both Clove and Nephytos were aware if this fact since they were informed during they amnesty.
The latter don't believe for a moment Eggman is gone while the former is too worried about her sister to think about this. I don't know if Jewel is aware of Mr. Thinker or not but if she's then is a high level secret and I am pretty sure the Restoration will send someone to check on Mr. Thinker and notice he's gone. Fortunate with the Warp Topaz Dr. Starline manage to make a clean gateway with the amnesiac Dr. Eggman so nobody will know what happened to him.
We have the advantage of anonymity for now and we should stick that way until we have a concrete way to take down the Deadly Six in a quick and efficient way without destroy most of the badnik horde and factories.
They control the entire of Eggman's army and everything the doctor built and they have a bone to pick with Dr. Eggman if they caught a whiff of our return. I for one don't face being bombard by the Egg Fleet, also yes they have control of the Egg Fleet.
That's why I think hacking the Egg Net is a bad idea since even a bare failure would be enough to alert Zavok of our current location.
The Conch is a priority to acquire before doing anything else since it could cripple them in a fight but since the effects only last as long the wielder lungs is not nearly as the silver bullet as we like but still powerful in a fight.