As a Las Vegas visual artist packing paintings for shipment across the country is something we come across on frequent basis. It is truly a stressful processes until you get it down or until you find a great Las Vegas packing company.
The best way and safest way to ship art or anything fragile of a price point of high value would be wooden crates for shipping. Most crates are made out of wood and can be custom builts and made.
You can build your own crates but it does require a number of tools and most likely a truck to buy the wood ply board and bracing you would need to make it. Check out How to make your own crate by Kate Vrijmoet if that is something you can and want to do.
The cardboard and bubble wrap is another way here is a step by step guide on how to pack your paintings by Agora Gallery.
I hope your art shipping goes well and that this can help.