I've had machines wrapped in about 8 layers of bubble wrap that has very small bubbles, and that seems fine. I've had it packed with large bubble stuff, with poor results.
I've found the number one thing is make sure the machine can NOT move around, not up, down or side to side. So far I've bought and had shipped 23 machines, and have seen quite an array of packing jobs.
1. remove anything you can remove, the machine is heavy and will break other things like lights if it ends up on top of them (like laying on it's side). Don't leave anything "loose" that can move around and scratch the machine (like control pedals, or attachment boxes). Over wrap them and make sure they also can't move around.
2. if the machine can move at all, it will. Mostly I've seen them packed so the machine can rock back and forth, this will bend all sort of interesting things.
3. if there is a case, either pack them separate, or make sure the machine can NOT move around inside the case. I've ended up with more broken cases from the machine moving around, and had one end up upside down on my doorstep, so the machine pulled free of the case and made a mess of things. The machine is rarely damaged in this situations, but a thin wooden case is no match for a 25lb machine. The ones that survived were either packed separately, or the case was stuffed so full that the machine was fully supported inside the case. The only real safe way with a wood case is to pack them separately - otherwise you are only hoping you get lucky and it does not end up upside down at some point.
For me, double boxing isn't a big deal, provided there is unmovable support around the machine. I've had several with packing materiel that moved aside during transport, and the machine had parts sticking out of the bottom of the box. Had one the Postman said they taped back up at the station because it was part way out of the box already. And that was from the bottom of the machine rubbing a hole through the cardboard.
I think I've only gotten two machines that were double boxed. That is the best way to insure the outside padding does not move around.
BTW - many years ago I ordered a rather large picture in a fancy frame. It was wrapped in plastic, then set in a bed of spray foam around the edges of a box, which molded itself exactly to the frame. I was worried that large a piece of glass wouldn't make it safely, but the seller assured me they shipped a lot of framed art successfully.