There is no plastic 1/350 CVL, which means no cheap one. Without going into the economics of resin casting it is very unlikely you will find a mutli-media kit of this sized ship for less than the one you saw on eBay, unless a modeler is just looking to dump one.
As far as scratchbuilding, that would indeed be the way to go for you on this project. Why not give it a shot? You can get good plans from the Floating Drydock
http://www.floatingdrydock.com
And supplement them with photos that they sell as well. They are an outstanding resource for anyone who is building a WWII US naval ship.
If you have no experience in scratchbuilding, I would suggest picking up Mike Ashey's book on Ship Models from FSM; the last few chapters cover pattern making in this scale which would be very applicable to your project.
Good Luck!
Kurt