Fix broken flapper door

While installing a new mode selector actuator, one of the plastic arms for one of the flapper doors broke flush. Local repair shop wants $2,000.00 to fix, because entire heater core box has to be replaced $900.00 from Subaru (Subaru doesn't sell a repair kit or just the door). Was quoted 11 hours of labor, because the dash has to be pulled off. I would like to attempt this repair myself.

My question is, if I can find just the flapper door, is it possible to replace just the door without removing the entire heater core box (once removing the dash)?

Thanks