If you are doing oral antibiotics this can be very hard for a cham that is already physically compromised and in a stressful state. Depending on the antibiotic some can effect their organ function.
Then you add in forced feedings and that is another stressful intervention.
I personally would not move him into a new cage right now. Connect the mistking to the current cage. You do not want to trigger more stress by putting him into an unknown space. He is too compromised. Why move into a new room? If it is a calm space I would not bother. I have had chams react to moving into a new room just based on how many more window and light came into the new room compared to the old.