Since they're nice and flat I would lay the machine on either side. The top panel hangs over the back a bit on both washers and dryers so that's a no go, and the front panels on both machines have a slight curvature to them so that's no good as well, at least that's my opinion.

Yes either side or even the back is best, I would NOT attempt to remove the glass control panel when moving this washer, just don't handle the machine by the control panel when moving, lifting etc. Just tape the lid closed and provide and old blanket or other padding to keep from scratching the finish.   John.

Do you mean to say you're leaving a hand truck or dolly under the machines while they're being transported in the back of your truck? Or have I misunderstood you?

I prefer to move Maytag machines carting, and if I must lay one down for transport, on the left side as you are looking at the machine straight on.  I do this because the motor is in the front left corner and the whole Maytag machine's center of gravity sits a bit to the left because of it.  In the grand scheme of things you can't hurt the mechanism of these machine even if they were transported upside down!  I personally hate moving them on their back because of the top overhang and the drain hose.  

Maytag used a "shipping block" when they shipped them new. Either a plastic piece, or a Styrofoam piece, that fit into the tub opening, and held the mechanism in place. It might be worthwhile if you could locate one.