Fed Ex is cheaper than UPS - UPS is expensive! Sometimes twice as much as USPS. I use USPS Priority right now too but we will add the others once we get our new system going. You could check into Parcel Post? It's 3-10 days not 2-3, but some people don't care about speed and if they do, then let them pay more! I am learning the hard way that you can't just give everything away. The answer might be that you have to charge more for the product or more for shipping.
Could you send the beds un-stuffed? It's easy to find poly-fill or even buy pillows and use the stuffing from the pillows. That's the easy part. It's the sewing that's the hard part (I am currently banned from using the rotary cutter due to nearly needing stitches....
) Maybe give people the option of paying more for shipping or stuffing themselves?