I bought my tail off of VAF and it was shipped via Forward Air fairly reasonably. They don't come direct to your home. You pick it up at a their dock which hopefully isn't too far from your house.
The first thing I have is: are you talking about fully assembled parts or just kit parts? Insurance could be the issue. Of course, a completed elevator is worth more than small pieces.
Second, don't even think of telling them that you are shipping "aircraft parts."
I called Van's and believe I talked to Barbara (years ago) and she told me to have it shipped under something to the effect of:
(Code number ??) Miscellaneous aluminum bar, angle and sheet.
I had this problem when I bought a wing kit in Virginia and had it shipped to California via ABF. Good luck.
I shipped an entire QB fuselage kit from Carson City, NV to the Atlanta area for well under $1000 including insurance. There were two large crates and I recall the total weight being around 1000 pounds.
uShip is a bidding service and various freight brokers will bid on your shipment. My shipment actually came on UPS Freight. Once you accept an offer, you can communicate with the specific broker for pickup and drop off info, plus special requests (like insurance). It wasn't pain free as my broker was in Miami and they did not speak good English, but overall I was satisfied and would use uShip again.
If you can hold out, the offer prices will get lower and lower.
I mailed a Citabria rudder from Detroit to Anchorage, about 7 years ago, by Parcel Post. $125.00. Wrapped in heavy corrigated cardboard, reinforced with some 1 x 2s inside. USPS Parcel Post is not very speedy but it arrived untouched, and the lowset cost.
I recently, as in two weeks ago, had a James cowl shipped from ky to wa . It wasn't heavy but the box was huge. FedEx wanted $400 and ups about the same. I plugged the numbers in shipxfreight.com and was able to ship fedex freight for $180. They came and picked it up from a car dealer business and dropped it off at an FBO a few miles from my house. Was absolutely no hassle and on time.