NEW - Point of information: Please note that once a barrel has been nitride (as in the case of Barrel #1) it is more difficult to adjust headspace as the surface is substantially harder. That said, there are at least two approaches to obtain the desired fit:
1. I will sell you the associated reamer for an additional $100 and you can use it. Yes, that reamer's useful life will be reduced. IF you are going to repeatedly rechamber the same barrel, at some point it may need to be reconditioned – Pacific Tool and Gage, the maker of that reamer, charges $98 to recondition a reamer. If, however, you are going to chamber a non-nitrided second barrel or, for example, use that reamer to cut a case length trimmer like Little Crow's WFT case length trimmer, you are all set.
2. The barrel-to-action fit can be adjusted by, as applicable, shimming to fit or, if your action has the typical Rem 700 style front recoil lug, that lug can be surface or Blanchard ground to fit (as close as a .0001). I suspect the cost to do this is less than the $100 for the reamer but I have no hard numbers. Several companies offer Rem 700 recoil lugs, including Holland ($35-$38).
Bottom line, if you have been told that this is an impossible situation, that is simply incorrect. Does it take more effort, and add to your cost? It does.