I moved my previous plasma after purchase in the rear of an SUV while laying on it's back about 40 deg. against a bunch of soft blankets and covered by one also. 150 miles. No problems whatsoever.
We just moved it again (8 years later) and I knew I would be replacing it soon but still trusted it to the movers. It was mounted on an AV stand and very easy to unhook and re-install.
But it was heavy about 80 lbs compared to it's 45 lb replacement.
The movers handled it very carefully, as I saw it disappear into the truck. 3 hrs later they carried it out and remounted it. It worked perfectly and not a single blemish or fingerprint on the screen.
I would take a leap and say 'most' reputable movers know how to handle a flat screen these days. They would have to live on another planet if they did not. But I would probably quiz them a bit if mine was still relatively new.
Samsung PN51F8500, Emotiva MC-700, Outlaw Audio 5000, Xbox One S, Dali Ikon 6, Vokal 2, OnWall, Outlalw LMF-EX, Furman Elite pf15i. UTurn Orbit Turntable, Ortofon 2M Red cart. and a Vincent PHO 80 phone preamp.