I like the feedback here and I have another bit of info, based on my experimenting so please take it for what it's worth - opinion based on a few experiments.
To begin with, a friend of mine who apprenticed at G&H and then went out on his own and has an established business building high-end rifles, has asked me numerous times to thread and chamber rifles that have metric threads - his lathes are old American iron and don't give him the option of cutting these "darn" threads. One of the first jobs I did for him sent him into a tailspin, using my gage pins for alignment.

He said it wasn't worth wasting time on this- his barrels were close enough ID to OD. I've shot a few of his big boomers and if you can bear down and hold center, they shoot exceptionally well at the distance they are designed for.
Now, in some of my own smaller bore rifles, sitting at a bench, shooting high power, exceptional glass, all the rigging to go with it, on a good day, I may be able to tell the difference at a 100 yds between a perfect chamber aligned barrel - and one that is skewed... I know a few shooters that can tell me there's an issue and I've been a witness to it.
Then, a slow moving, large caliber that goes sub-sonic at 280 yards, throwing a cast bullet and tries to hit a target or gong at 1000 yards, that chamber that runs out .001 or .002 to the bore - few could probably couldn't tell any difference.
In the schuetzen game it may show up slightly shooting off the bench, probably not if one is breech seating and definitely not noticeable in the offhand game.
S-P,
your situation is a case where having a set of -plus/and/or minus- gage pins would benefit. Plus generally run .0002" larger and minus pins will run .0002 under... do they warrant having for this? - NO. Your runout will be fine.
Bob,
In the case for the muzzle, I'll have slugged the bore 3 or 4 times finding the tightest spot, then cutting the barrel off at that point. A gage pin that fits this close is preferred, and I'll slide it in and out the inch or so I have to work with, checking it at a couple points and then machine my crown. -close enough. On the better barrels, I rarely notice any change. Had a few that didn't cost as much and there are some questions raised.
I have a very nice B&S cylindrical grinder that will make absolutely wonderful gage pins but setting up and making them isn't very high on my list of priorities so I tend to use what comes in a box.
5¢ worth
Greg