Bob
It appears that your on the right track , if the problem is while driving the air governor controls both the unloader valve in the compressor and the purge valve in the air dryer.
The braided air line you referred to is the air discharge line from the compressor to the air dryer the air passes through the air dryer and exits through a check valve in the dryer before running via a air line ( usually green ) to the wet tank.
If the check that valve goes bad or sticks the air can leak backwards through the air dryer when the compressor is not pumping
To check that check valve disconnect the braided air line with air in the tanks and engine shut down and check for air leaking from the dryer connection.
When you replaced the old braided discharge line was there signs of excess oil passing from the compressor?
With all the work you've done now might be a good time to clean and service the air dryer .
The links below should help you to understand the operation of the governor, unloader and dryer operation .
Your coach most likely does not have a Bendix air dryer but the operation will be the same .
https://youtu.be/bmgSwSeLk_o?si=Cr926sIOiIVIZv5Fhttps://youtu.be/7phjlysl7Zo?si=9kMvxbicFKKgDI5tHope this helps
Eric