Kind of a long shot, but does your coach have vacuum switches for your dash air controls?
Many gassers do, but I've no idea about DPs. Vacuum controls can cause the problem you describe. I had 'em in my previous (gas) coach.
Vacuum controls work by applying or releasing vacuum to "vacuum servos" to move the flapper valves in a dash air system. There is one that opens or covers the various outlets that send air to the floor, dash, and windshield and another that "blends" hot and cold air between the heater core and the A/C core.
The last one sounds like it could be your problem.
Problems arise when there are leaks in the vacuum lines. As long as the engine is pulling a good vacuum everything works, but as soon as it's under load the generated vacuum drops and affected flaps go to their default position.
Leaks can be caused by pinholes or cracks in the vacuum lines, lines that have come off their fittings, or problems with the vacuum accumulator that such a system will have. No idea where it'd be in a DP, but probably somewhere near the vacuum source on the engine.
The accumulator's job is to provide a reservoir of vacuum (weird concept, I know) to keep everything working when engine demand causes generated vacuum to drop. Leaks don't let the accumulator build up the needed reserve.
In my previous coach I had a line come disconnected from the outlet selector switch causing the direction flapper to send everything to the windshield, in the spring, in the deep south. I was able to work around the problem by disconnecting the return spring on the affected vacuum servo and set it manually to send air through the A/C ducts until I could get it fixed.
Of course, if you don't have vacuum controls all of this is entirely irrelevant.