I can't answer the part about who can build a rifle for you,I live in Australia,but I can give some advice concerning WHAT to build.
I do this for a living,amongst other things.
You'll want an action of very rigid design if you want it to be super accurate.Remington actions are very good but not necessarily the BEST.
Before you undertake this type of project,it is very important to speak to a few people that have had this done before,and ask them who did it for them,time it took,cost,what they purchased first in regard to action,barrel and stock.A good place to find out this stuff is your local range.
Winchester Pre '64 are preferred,but Post '64 Classic actions will do.I don't know how much money you want to spend,but there are actions from places like Dakota,Granite Mountain Arms,Kimber and Ed brown custom.
The calibre you have chosen isn't a true long range round in my opinion,depending on whether you're going to be shooting further than 1000yds,I feel you will need a larger calibre that shoots heavier bullets fast,338 Lapua,338 AM,338 Edge and 338-378 Weatherby spring to mind.
In 30 cal,300 Win Mag,300 Weatherby Mag,7.82 Warbird and 300-378 are up there also.300 RUM is an unknown quantity to me but figures support it for this type of work.
As you can see this is a big undertaking,what I have advised you is what I advise my customers.I want your business,I'm NOT the best person to ask these questions,nor is any gunsmith!
You really need to speak to HAPPY people that have got their project in exactly the way they wanted it when it arrived.
All the best!