Re: What can I expect to pay?
Unless you are planning on $900+ for the job, you will want to call Jim at NSS and get his Savage style barrel for the Remington action that uses a locking nut. That would set you back about $330 + another $60 for the nut and recoil lug. If you like it, you can always later strip it down and send the receiver to a specialist to get it trued.
Right now, receiver trueing by some of the name brand shops has a very long lead time. Ordering and fitting shoulder headspaced barrels has a very long lead time too. I ran out of patience trying to get my own Rem 700 done that way and got rid of it. The benefit you get with a Remington is a lot more trigger and stock choices.
For removing the old barrel, I recommend having a local smith use a parting tool just back of the shoulder and cut about 0.060" deep, that will take all the preload out of the shoulder and it should be easy to get out the action. Factory barrels (brand new takeoffs) are usually not worth more than $50-$60 so unless it is a new stainless barrel, it will cost more money trying to save it than using the parting off tool trick that will get it off fast.
If you need help with assembling Savage style barrels with nuts, drop me a line, I have all the tools and should be within driving distance.