Did your local smith recut the receiver threads? He may not even have told you that either way. They should have been recut or the entire accurizing process and $$ was pretty much for not in my opinion.
I assume he used an aftermarket recoil lug, this big 300 really needs a good solid footprint so there is no flexing.
The throat length you discribe does not bother me as much as what the diameter of the throat may be. A long throat will generally not produce an extremely finicky rifle as long as it is cut to the proper diameter. A loose throat will cause all kinds of headaches.
It would take about 20 minutes to check if the receiver was trued properly by pulling the barrel and taking some depth measurements off the receiver face to the bolt face.
With a chambering like the 300 RUM, everything has to be square, everything. If they are not, the variation in groups will magnify with a large chambering compared to a smaller one. There are reasons its relatively easy to get a 308 WIn to shoot tight groups and why its harder to get a fine shooting BIG rifle. The machining has to be as perfect as you can get it.
Do not read this as me hammering your smith because I am not but there is something wrong with your rifle if you have that much into a custom rifle
and can only find one load that is reasonably consistant.
With my rifles I shoulder fire test them at 100 yards to prove they are capable of at least 1/2 moa accuracy for three shot groups. After a proper barrel break in, they generally will top this by a fair margin.
A rifle built using the componants you list should not be difficult at all to get to play with the 1/2 moa range easily with a decent selection of bullets.