I would suggest looking long and hard at a 300WIN MAG for 6-700 yd ranges.
Everybody has dies, lots of good brass, it's easy to load for & capable of extreme accuracy. Of the ones on your list I would say the 300 RUM would be hard to beat.
Personally I'm not a fan of the weatherby's, Jarret or the STW. This does not mean they are not great chamberings, but if we all agreed there was one perfect chambering we wouldn't have any of the others
When I'm picking a catridge these are some of the things I think about.
1~ What velocity and bullet weight do I want out of this.
2~ Is price a deciding factor or am I going all out on this one and buying exactly what I want
3~If price is a deciding factor
A~ is there good brass available.
B~ Am I going to have to put a lot of work into the brass.
C~ Am I willing to put the work into the brass. If not I would be better off with something I didn't have to put much work into.
4~ Are there good readily available dies at a price I am willing to pay for them.
5~ Do I want a repeater or a single shot.
If a repeater, am I willing to pay the extra to get a super long case to feed. If so what's available for making the case feed.
Hope this helps a little with your decision making. To be perfectly honest all the calibers you mentioned are all perfectly capable of harvesting elk at 6-700 yds.
The prices from your gunsmith are on the low side .