I shipped some SBF heads a few weeks ago. I built a small crate for each one. I built it out of 1x1's and 1/4" luann plywood. It had a 1x8 or 10 for the end. It came out nice and only added 5 or so pounds to the total weight of each head.
I used the 1x10 for the ends and the 1x1 for the frame to connect the ends together. I mounted the head with screws to the frame inside and covered the entire framework thing with the 1/4" plywood.
FWIW too, I shipped these from work using my work's UPS acocunt. I ship everything this way. UPS charges us by weight only! It cost me $25 to ship these heads.
We have an account with UPS at work. We have the UPS supplied scale, computer, etc... We ship by weight only. I've shipped some mounted rims/slicks with no problems. Very cheap. I've never had to enter dimensions. There is no area to enter them in on the screen, just shipping address, weigh it and click away.
We may be set up this way since we usually ship a couple hundred pieces each week via UPS.
ALSO, I did ship some BBF heads a year or so ago. I wrapped them like Paul recommended and FedEx charged around $45 each. Hope this helps.
I haven't been coming on here much anymore as my BBF projects are all "done", but holy cow, is there any moderators left? I'm trying to help out by reporting spammers as I come back, but wow, there's a TON of them, and it seems like some that I report go unnoticed for days or weeks.