For a move that far, less than $1,000 is probably as good as it is getting unless you can borrow a truck or something. One thing you could, I guess, is buy a super cheap truck/van and drive it to CA, then sell it, but the transaction costs might be too high.
Wha? Disagree. I know it's shorter, but I moved 700 miles eight months ago, and the truck rental was less than $500. I also rented a 16 footer, which was way bigger than I needed, and I was also bringing a couch, large bookshelf, and queen bed.
OP, I strongly recommend 1) checking to see if you are a member of any associations that get discounts on truck rentals (pretty common, actually) and then 2) seeing if you can get the companies to beat their competitor's price.
I had potential discounts through my bank, a credit card, and my state bar association. I figured which of the three gave me the best base % off (the bar association). Then I got quotes from Budget, Penske, and ... some third company I forget the name of. Each one of them offered to match the lowest quote, and some of them threw in some other freebies to sweeten the pot, like furniture straps for no extra cost. You will get lower quotes if you move during the week, not on a weekend, and avoid holidays (I hope you're not moving on Labor Day with a September move!).
For how little stuff you have, you could probably fit your stuff in a 5x8 foot trailer (assuming you have a car that can tow one). I just did a search on uhaul's website for that size of a trailer from Chicago to San Francisco during the first week in September - the website quoted me $427.
Another idea: I bet you could fit your stuff in a minivan. I did a quick search for rental cars on Kayak, putting in a pickup point in Chicago and dropoff in San Francisco, for the first week in September (avoiding labor day). It looked like one could be had for $543. This would be a decent option if you don't also have a car you need to take with you (otherwise I'd probably go with a trailer).
Final piece of advice: you need to donate some of your books. I know it's rough; I'm a book lover as well. But the reality is that they are a huge pain in the ass to move, and someone will love your second hand book as much as you ever could.
Final Final piece of advice: remember that ordinary moving costs, including truck rental and mileage, are tax deductible. Keep your receipts!