I'm not sure what the problem would have been with transporting your rig on the flat bed. I have had two buses that I was driving hauled on a flat bed and had no problems. One was a 1978 GMC Buffalo that had a plugged fuel line and we put it on a semi flatbed and hauled it from Buttonwillow,Ca to Bakersfield and the other was a 45' tour bus from the Dalles Or to Portland. Never did hear what happened on the latter,but I had an ungodly vibration from the rear somewhere.
The Bakersfield tow was fun as the driver was a little guy and pretty much of redneck and he took me to breakfast at the Crystal Palace,Buck Owens place, when he found out I knew Don Rich, who was Owens sidekick till Donny died in '73.