It would be less hassle, and possibly cheaper to just get an entry-leve gun with the action you want, and part out the pieces you don't need. Get a Remington 700 SPS, and sell the barrel and stock, and maybe the trigger assembly too if you decide to upgrade. Ditto for a Stevens 200, and you get a Savage 10/110 action.
Or check with the gunsmiths for customer actions - Bits of pieces has some, as stated above. Prices will be a lot higher, and when you factor in the price you'd get for the take-off parts, it's higher still. But you do get a custom piece for your money