Heehee! I did it!
The rest of the game was pretty simple: After the really hard part of getting the Syreen ships out of Ur-Quan space, the rest was fairly simple. I faced down the 5 Mycon Podships guarding the Sun Device. (by now, I've taken down quite a few of them with Pkunk Furies, so it wasn't too bad) I traded the Burvix 'Caster for the Rosy Sphere, (easy) took out the Umgah guarding the Dnyarri with my Druuge Maulers, (I lost two Maulers, but otherwise, also not too bad) I picked up the Aqua Helix from the now dead Thraddash, (also easy) got the broken Ultron from the Supox, (easy) fixed it and gave it to the Utwig and fought the five Druuge Maulers for the Utwig bomb. (took out all 5 with my starting Earthling Cruiser and only got hit once! Easier than I expected!) And then, I visited the Chmmr, they transported me back to Earth, and...
And when I faced Commander Hayes, he started saying all the stuff he says when you meet him the very first time, complete with flickering lights and everything.
And the configuration of my ship, visible at the right, showed the Utwig Bomb and Chmmr crystals in place. The trouble is, since I now have unlimited RU and no Storage Bays, the game doesn't register that I have any radioactives, so the game is in an infinite loop, where Hayes keeps asking me to get the radioactives and I can't do anything. (He still gave me a free lander, though, the same way he does if you lose your lander at the beginning of the game) So... I guess I have my answer, then.
Maybe I should download UQM so I can do it properly.
EDIT: I tried it a couple more times with this version, first with delivering the radioactives before visiting the Chmmr, (at which point it went into an infinite loop, telling me to go visit the moonbase and I can't do anything) and then, delivering the radioactives and visiting the moonbase before visiting the Chmmr. This time, it actually seemed to work properly, except that the part where I'm supposed to face the damaged Ilwrath ship at the beginning, the screen flickered, and it flipped back to Hayes and he continued the dialogue as if I had just destroyed the Ilwrath ship. Then, I got treated to (almost) every bulletin in the game at once!
Each bulletin was separated by Hayes saying "Also..." so he used that word a lot.
(8 bulletins in total) Curiously, he didn't give the most important bulletin about the Utwig Bomb on my ship!
Also, there was one bulletin I didn't recognize, in which Hayes remarked that 6 of his crew members suddenly fell unconscious at once and, after they recovered, reported a feeling that something very wrong had taken place, and the only correlation the med techs could find was that they all had high esper potential. Huh! I wonder what I did that triggered that?
Was it the Shofixti trading? Or maybe it has something to do with the Dnyarri? Hmm...