Check in. We were hoping there would be a luggage bag but there is nothing with the dimensions we need for this huge chassis. We no longer have the box cuz it's been a few years now. Why remove the gpu?

the checked in luggage are thrown around so better remove gpu in PCIe slot and mechanical hdd.  an old Mac Pro box might be large enough for A51.

Hardigg Pelican Hard Case AL5430-3006

al5430-3006- single-lid-hardigg-case

https://www.ebay.com/itm/203103446497?

shipping cost of this used empty box is insane.

my Mac Pro 1,1 original box dimensions 27.5 x 23.0 x 12.5”

Would be perfect for Area 51 R2-4 

Height: 569.25 mm (22.41 in)
Width 638.96 mm (25.15 in)
Depth 272.71 mm (10.73 in)

you could ask around on your local Craigslist to see if there is an Area 51 R2-4 owner who still has the original box and willing to sell it to you for $40 or something like that, or a classic Mac Pro tower box for less.

or you could buy a heavy duty double walled cardboard box like 30x30x16”.  but these are usually sold in pack of 5 on line and cost quite a bit.  If your local UPS store has one like that, great.

https://www.uline.com/Product/Detail/S-20415/Heavy-Duty-Boxes/30-x-30-x-16-275-lb-Double-Wall-Corrugated-Boxes 

https://www.ebay.com/itm/115372546117?hash=item1adcbd5845:g:LlUAAOSw47hidE4~

I would try the local UPS store, usually they can sell you packaging materials or  have them do the work and even ship it.

I would look at the value of the machine versus the shipping costs. I am assuming this is a permanent move.

My suggestion is to sell it and purchase a new machine at your destination location, rather than dealing with the headache of shipping it.