I think killing the eater has a chance, and that it is our only chance for success, and to minimize the risk of that just killing whoever attempted it, it should be a zombie.
If the eater is not killed while changing bodies or something, then it is going to posses one of you again. There's no escaping that.
((There are only 3 real potential actions. We can do some of them in combination, but it boils down to:
A.) Get the Eater to the Pit. With the angry sun coming down on us, I don't believe we can outrun it. You (Tir) might have a chance with your MK3, but I don't know that you could make it and we've got people doing stuff to the Eater already.
B.) Kill the Eater. Instructions were to kill the Eater at the Pit, and we know that killing the Eater was a risk in the past (how many people has it possessed of ours because they killed it? Three?) I like this option, and it might be close enough, but I wouldn't ask you lot to do something I'm not willing to do myself (though Mummy goons would be a reasonably safe bet, I think). If we have a volunteer, make it known and make it happen.
C.) Run Like Hell.
It might be that giving the Eater to the sun is a win, it might be that it's a loss. I don't know. What I DO know is that there's no way in hell we can stop the Sun; and I get the feeling it's not gonna stop even if we guess "right" on how to handle the Eater. It's time to make a call and get the hell out of the blast radius.
I don't know that anyone besides Tir could do A (and even that's a crapshoot), so our options are either B+C or just C.
You're forgetting option D.
Go on the offensive. Kill the sun.
If you can't provide Steve with coordinates so that he can hit it with a kinetic strike, you could probably use your extensive arsenal against it. Doesn't any of you have any oversized death weapons they could use to kill a god? Any nukes or similar?
Or just try shooting it with gauss rounds, maybe that will be enough to make it think it's not worth it or at least slow it down a bit as it strikes down those annoying flies.
EDIT: And I'm really not sure if C is an option. Wasn't this entire desert created by the previous eater or rather when the Sun ate the previous eater? Doesn't that mean that anything in the same country as you is probably screwed?