I have shipped Morning Glory type horns with 100% success on 5 different occasions now by using this method: (I've saved the best for last.)
1.) Cut three heavy cardboard circles 4" larger in diameter than the wide opening of the horn.
2.) Turn the grain of the cardboard circles perpendicular to each other as you stack them, & "cross" duct tape them together
tightly.
3.) It is not necessary to affix horn to cardboard. Beginning at bottom, using two people, lay a 1&½" thick foam rubber that you
cut into circle with a ⅛ or so sized wedge removed from it (like a Pac-Man). Use the height of the horn as your radius and go
3 or 4" over your horn diameter to determine the approximate width of your wedge-(Remember it's easier to cut a little excess off
than to make some up!). Cost of Foam Rubber- $20.00 (in Southern California).
4.) Wrap and affix the horn very well to stacked cardboard base at this point. Use packing tape & do not apply it to the horn itself- only the foam rubber and cardboard. You need not be an artiste here- the USPS will have to
send this processing manually anyhow, so there's no chance of it gumming up their machinery. When you're finished, your project will look like a small grey, white or green tree. Label w/ the usual "Handle with Care & Fragile" Labels.
5.) You can now send this via USPS Parcel Select and it will cost you or your buyer less than $35.00 Insured!!!

It sounds a bit crazy, but my buyers have all received their expensive horns in A-1 condition!
Thanks for reading,
Best of Luck,
Stephen