Thanks for the suggestions.
I did a complete overhaul of the bins and everything on Monday night. I hand sorted every single adult and large nymph and anything that even had a missing leg or walked funny or anything I tossed out. I was still able to save probably 75% of them, since they appeared healthy and could still move quickly. I'll continue to sort them out once a week or something to make sure I'm keeping only the best.
I've also separated everything based on size for the most part. Adults to their own bin, large nymphs to another, and small nymphs in another to make it easier for me to use them as feeders. I figured this will help me to monitor how quickly they are dying off or growing.
I did notice that almost all of the roaches that were dying were adults, because I have hundreds of large nymphs that are ready to molt into adults soon. It may have just been the demographics of the colony, and the adults were just at the end of their lives anyway.
The flies are also slowly going away already too. I've only seen a couple in the past few days, so hopefully that is all under control.
Again, thanks for the advice and help. I'll keep you all updated.