Hi, I'd caution you against
bikeflights.com. I shipped my bike with them for an event, and it was a disaster. They basically take your money and send you a fedex label. They do get a bulk discount, but if you make an account on Fedex.com you'll get the same price within a few dollars, but you'll be able to change or cancel the shipment details at your leisure, and you won't have to wait for the bikeflights guy to process your order. In addition, with bikeflights.com, you are prohibited from filing a claim with fedex. You have to go through bikeflights.com.
I tried to file a claim with this fellow, but he told me by looking at the image of the damage I sent him he could tell that the H3 wheel had been damaged and repaired previously. What would it matter whether the a new or a repaired wheel was damaged? Unless there was evidence that the wheel was damaged before shipping or that it was improperly packed it's irrelevant. He gave me a lot of other hokey run around too. I had a strong case because the shipping box was hugely damaged. He eventually let me use his carbon repair guy at no cost. However this took over 7 months. Months went buy without responses to emails. For a while I thought they had lost the wheel. I'm also skeptical about the quality of the repair.
No way would I use bikeflights.com again. Print your own label on fedex.com. If you've made an account and there's still a big price difference, make sure you're comparing apples to apples with declared value, box dimensions, and weight. I found that a bike box can easily be a bit bigger than what bikeflights.com lists as a standard bike box. The important thing is to make sure length + girth < 130 inches as that bumps you up in price quite a bit. When I did booked I found my cost to ship was much greater than what the little estimator tool on their website suggested.
Also, there's no way I'd risk shipping via fedex in card board. I'd get a proper hard case. The extra weight won't cost any extra at those dimensions. I've been fine a few times, but I had one incident, and that's enough.