Don't be intimidated by the FedEx rates, all the private companies charge insane amounts. the USPS (there are all kinds - priority mail, first class) should charge something in the range of a few dozens of dollars.
I'm sorry, I thought I mentioned there's no use checking with FedEx UPS and the like, but I didn't, perhaps it was in the PM that got deleted.
I could try to find out the exact price online if I had the dimensions of the package.
As for gift, you've got it right.
Thanks for the effort.