Welcome to iRV2 .
There have been a number of similar posts over the years ; but usually required chassis battery disconnect to shut the engine down .
But then I can't say if they had tried using the trans shifter .
From your description , it would appear there is enough voltage to keep the engine ECM active but not enough amperage to activate any transmission functions .
Can you try using the turn signals to see if you get the same shut down ?
Similar issues on Freightliner chassis , traced back to a defective diode in the alternator activation wiring . Another member found that his cross over between battery power and ignition power was due to internal issues with his dash radio, that allowed the power for the radio memory to cross over to keep the ignition side powered up .
To eliminate the radio as a possible cause , pull both the fuses that power radio function, or disconnect the wiring from the radio.
Is your coach on a Roadmaster chassis ?