If you had to move it across town, or a short distance, under 100 miles, I think I say take a chance. 2000 miles. Get the right rig or else hire it done. You don't want to have a disaster and be that far from home. Or have a braking/trailer/load issue going 70 on the interstate! That takes the fun right out of it,not to mention is flat dangerous.
I have had luck, although I didn't end up using them, finding some good prices on shipping through a website called
www.uship.com. Set up a user account and post what you are needing shipped. Know the total weight, length, width, and height. You can specify how it needs to be shipped - enclosed, open, etc. as well as the pickup/delivery window. I found that if you are very flexible w/ pickup and delivery, the price goes down. A lot of these guys have regular runs and need to pickup backhauls. It also helps a lot if it rolls and runs. You will need to specify that as well. You can even call the guys hauling it and visit with them about it.
My quote for hauling a 3800 dually flatbed home from Wichita KS to Central Texas was $600. We ended up making the trip ourselves with a 20' car hauler gooseneck. With fuel, tolls, and food, cost almost $350. And a very long saturday. on the road 18.5 hours. But it was an adventure! Best of luck with whatever you decide.