This simply isn't possible.
Galen and Dureena had a big arc developing, that was central to the premise, you really couldn't replace those characters.
You can't do the show without a Captain, so therefore, you had to keep Gideon. If push came to shove, you could replace the actor (though it certainly wouldn't be my first choice).
Eilerson was simply awesome, and makes total sense that IPX would want a representative on board the ship
It would make absolutely no sense to the premise of the show early on (Searching for a cure) to be doing so without a Doctor on board, so, again, if push came to shove, you could replace the actor, but, you couldn't eliminate the character
So, that's 4 characters right there that you couldn't do the show without, and as wesome as Eilerson was, and his connection to IPX, it would be foolish to replace his character.
And then of course, Matheson as Telepath, although they didn't use him much up to that point, having a Telepath on board opened up some interesting story opportunities, and since the Captain was meant to leave the Series in Season 2, you needed to have someone in charge when that happened. Daniel Dae Kim was just too beautiful a man to replace the actor