In my limited experience with shipping large things long distances cheaply,
Fastenal seems to be reasonable. You have to deliver the item to one of their stores on a pallet. If it is an enclosed crate, they do a better job of guarenteeing no damage. An item like this would probably not be worth the effort of building a fully enclosed crate. So I would need to find a pallet.
Apparently they find space on a LTL (less than full load) truck going in the right direction to get the cheapest rate. It may be slow and you don't get a tracking number.
Just a guess, but maybe $100 +/-50 ?
Then it gets delivered to the Fastenal store of your choice. Here's a link to see if one is near you-
https://www.fastenal.com/locations
Now this doesn't sound too appealing, but the alternative is probably $500. I recently bought a large truck brake part from Arizona shipped via Fastenal. The genious junkyard just set it in a plastic milk carton- after all their assurance that they would take great care and make sure no fluids could leak out. Anyway, as poorly as it was "boxed" it made the 2,000 mile trip unharmed. So if you want me to investigate further, let me know.