This is the box, which you can get locally at any uhaul place.
https://www.uhaul.com/MovingSupplies/Boxes/Clothing-Moving-Boxes/Grand-Wardrobe-Box?id=6560
24" x 21" x 48"
24" x 21" is quite a large base and the 2-3 times I have shipped seats, it fit.
Then, cut the top down so that it is less than
UPS Large package surcharge:
https://www.ups.com/content/us/en/resources/sri/glo_lpks.html?srch_pos=2&srch_phr=large+package+surcharge
Large package surcharge:
Length + Girth which is ((2x width) + (2x height)) > 130"
With a 24"x21" base that is 24 + 24 + 21 + 21 = 90" girth
That leaves a height of 130-90 = 40" to stay below the large package surcharge
So get the height of the box down to 40" or below and save major $$$ on shipping. And each inch below 40 will save even more. At that size they impute a shipping weight that is way above what your seat actually weighs, you could probably even ship a single stock seat and stay below that level, although you would have to beef up the box somehow.