I've got a house full of those old beauties. I actually had a different Zenith 1938 model with the wire antenna running out the window hanging up in a nearby pine tree. I tuned it to WWL in New Orleans and plugged it into one of those automatic timers so that it came on in the morning. A 100 lb alarm clock!
Anyway, when I bought that same radio on eBay, the seller did exactly what is being recommended here. He removed the chassis and boxed it separately. Guess what. The cabinet got here safely but the chassis took a hit and it took a while to get everything operating correctly. Thank goodness for the replacement parts market that was alive and well.
As long as everything is packed well, you got no worries. But when you think about it, that big ole cabinet is a great packing box, ain't it? You just have to be sure it is screwed down tight. And I would definitely recommend removing the tubes and packing them individually.
I bought a beautiful Atwater Kent console on eBay and the seller assured me he was a "packing ninja". I found out he didn't know his ass from a hole in the ground. He left the chassis (extremely heavy) in the cabinet and proceeded to fill the cabinet with peanuts and wrapped pieces of cardboard around it and called that packing. In transit, the chassis ripped the screws right out of the wood shelf and pulled apart the wooden cabinet. Needless to say the tubes got smashed. And the dual speakers, which were just hanging from hooks in the bottom of the cabinet, came loose and knocked around. Not good for 60 year old paper cones!
My third part of this story is I found an avid collector in the state of Washington that was selling several empty console cabinets. I bought all 3 and he used an established packer (expensive) that built up a wooden pallet and isolated the cabinets from the packing with sheets of Styrofoam. It was worth the cost when I opened them up and found them looking just like were when they were packed.
You can't be too careful. It's not like you can go to the store and just get another one.
Gene