I know there's a post to Oreste below. . .

However, I've been trying to get the disabled Kr'Wgh fighter mission with absolutely no success. I've been flying a Rebel Avenger with a few escorts. BUT, did I screw things up for myself when, in a fit of frustration, I dominated Hera and Zeus, then released them from domination? Is there hope for me still?

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What you can try is to release them, get them back up to good standards (if you have worked for confed get role model card), and see if you can get the mission. If you can't stay there on Hera accept a mission, abort it then check the spaceport bar again. Or if you have enough money get escape pod and an auto eject button thing and kill yourself. Then you will be good in the whole galaxy.
See if that helps.

Kryptauros

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Your standing in line,
a very big line,
And you have a gun,
a Big Freaking Gun,
Gee now what do you do?