Welcome!
I'm sure the neutral TC mode will let the wheels roll just fine for short distances. The issue is possibly that the relative speed of the front driveshaft (zero) and the rear driveshaft (road speed) now appears across the transfer case clutches. Even though the clutches are not engaged, the relative motion is going to churn up the fluid, heating it up, and any residual friction between the clutch plates can damage them. Of course, thinking more, this is the identical situation if the front wheels are on the ground, unless neutral mode also engages the front axle actuator and then the front driveshaft is turning in the otherwise neutral mode and the only thing disconnected is the transmission.
A bit of experimentation would show if the front driveshaft is turning while rolling in TC neutral mode. Sorry I'm not with my shop manuals to see if they discuss the issue.
I think removing the rear driveshaft, or fabricating a tow bar adapter for your plow mount, are your only two options.
Also, does your tow dolly have electric brakes controlled by the MH? If not, that's a problem for many jurisdictions that limit the weight of unbraked towed things to 1500 or 2000 pounds. Perhaps your MH has brakes up for the task, but without self-powered electric brakes in the toad or the dolly, you won't have breakaway protection. That's a scary prospect.