+1 on Jim See's recommendations.
I would like to add, if it's a repeater application your building, ensure you look at other bullets (i.e. 208 Amax, 210 Berger) and make sure you don't throat your rifle to be a repeater for just one bullet. Your rifle may not end up liking 200 NABs as much as it likes 208 Amaxs or the 210 Berger or the Barnes or etc....
Since you've got that OAL tool...and are taking some measurements....take the longest bullet you'd want to shoot out of the rifle (if the 200 NABs didn't do what you want them to do), and seat it to working mag length, using the Jim See -.050 under mag box guidance. This is a dimension for two reasons...throat growth as the round count on the rifle increases....and it's a hunting rifle...things get contaminated, cold...you want it to work!
Now take a OAL ogive measurement.
Now seat your 200 NAB with the same OAL ogive dimension.
Then observe the amount of bullet intrusion into the powder charge, or vice versa, observe the amount of bullet bearing surface length in contact with the case neck....make sure those things make you happy with all your proposed bullets.
If necessary, reset your desired "go to" bullet you really want to use at a compromised seating depth.....now you have a dummy round that either your smith can use to throat your rifle or PTG can make a finish reamer for....and that throat/finish reamer will enable you to shoot (as a repeater) several bullets that've you've previously done the math for just in case your desired "go to" bullet and your new barrel have a disagreement
Barrels always win those arguments BTW
Good luck, and keep it fun! Your 300 UM is going to be a boomer I'm sure!