When I have to ship really bulky but light weight items I've found that Fed Ex ground is much cheaper than USPS Priority Mail if you have any dimension over 20". It's the only time I ever use Fed Ex. With a Fed Ex account number I think the more you use it the better the shipping discounts. At one point I think Etsy had a 'deal' with Fed Ex for slightly reduced shipping rates, so I'd dig through the Forums for more info on that option.
If you have the time Parcel Post would be a cheap option, but they can't guarantee a delivery window less than 9 days since they just put it on a truck. Parcel post for Hawaii and Alaska would take weeks as it's delivered by barge or driven through Canada. When I've shipped things to the East Coast via Parcel Post it's taken well over a week (I'm based in Colorado), so Fed Ex is way faster for the most part.