A couple or 3 of small things to consider.
Take out the front base screw.
If you are going to use a pipe wrench make sure that you are not turning the recoil lug. A action wrench is good hear due to the fact you pipe wrench will be squeezing on the barrel so they will need to turn together. I have been know to use the action wrench barrel vice and the nut wrench to do the job. Do not use the Ejection/Loading port for leverage.
If you have a high quality hone that is still flat, do the figure eight on the nut and the face of the action. Use the fine side of the hone.
Replace the recoil lug with a flat one. (Ground)

Varmint barrel of your liking and call Fred.The bolt work alone is worth the money.