Your theory is actually is actually solid. Her being a decoy does fit the mystery. If she really was brainwashed and trained to act like Kat then maybe she could be a decoy after all. I personally don't believe that Red is Kat but you theory does make me believe that the recent one that we were introduced to is a fake.
I agree with your theory that Liz is some kind sleeper agent. I personally believe that intel is vaulted in her memories via the many memory blocks. I have mentioned this on an another thread before.
As for this minor disagreement on whether the show can continue without Red here is my opinion. Red is a poster character from season 1 already and the show kind of revolves around him and Liz so I doubt that they can kill him off and continue the show. Technically they could kill him off but i think that fans will probably become disinterested and stop watching.
If i could ask were you a fan that was hoping for a Liz-Ressler relationship pre-season 8?