It sounds like you've had excellent airway clearance advice. You might want to ask your therapist the following:
-how much sputum do they need? I was once working with a therapist who was doing manual therapy on me and I coughed up a dime size sample. We sent it to the lab and it grew MAC.
-could you use 7 or 10 % just for the sputum sample?
-have you tried exercising before airway clearance?
-what about postural drainage? Many therapists don't like it because it increases the probability of reflux but sometimes it boils down to priorities
-what about using the smartphone autogenic drainage app?
-would a hand-held massage gun make a difference?

I hope this is helpful,
Linda Esposito