Couple of things: #1 unless you have a major need for 6.5-284 I'd go with 6.5x47 or .260 or something as the 6.5-284 is a real barrel burner ( I own one and it is great but barrels are not gonna last). Now, #2, with respect to the specific question: a perfectly excellent rifle can be built off a Rem 700 and I currently have ATRS and North Shore Barrels customs built off Rem 700 and as far as accuracy is concerned a properly trued up R700 attached to a custom pipe will be as accurate as anything out there. What a custom gives is a higher level of finish and smoothness as well as a certain pride of ownership. I have had customs built off - Defiance, Stiller, RPA, Barnard P and S and Swing ( yes, that old guy) as well as PGW ( yes, factory rifles but I will call them semi-custom).
What I'd do were I you is decide what kind of rifle you want (F-Class/PRS/LR on Crown/whatever) as, for example, a Barnard may well better suit a F Class whereas for example a Surgeon 591 would be the route for a more tactical rig. Then talk to a good gunsmith - there are many to choose from - and take some advice from them.