Since you're a Zags fan is it safe to assume you are in the greater Spokane area?
I only ask because the Godfather of the 338Edge (Shawn Carlock
www.defensiveedge.net) is in Rathdrum Id. which is just across the fence from Spokane.
BAT, IMO, builds the finest action money can buy. I don't see how you could ever go wrong with a custom build using a BAT receiver.
But, will a properly built 338 Edge using a blueprinted Rem M700 receiver shoot noticeably better than the exact same built rifle but with a BAT receiver, I'm going to bet it would barely be noticeable.
I look at full blown customs versus semi customs like this. If you already have a donor rifle like a Rem. Sendero and all you want to do is have the action blueprinted and rebarrelled to 338 Edge your donor Rem 700 was/is a good choice. On the other hand, if ALL you're going to use is the Rem 700 action and you are going to replace EVERYTHING else, at that point you may as well opt for the custom receiver too.
I've got both semi customs and full customs and I even have a semi custom that I had everything, except the Rem M700 action, replaced on. The semi custom that had everything replaced on cost me nearly, within a couple hundred dollars, of what my full custom 338Lap Imp, which is built on a BAT HRPIC, cost. That probably wasn't the smartest money I ever spent.
Built as a semi custom w/Rem 700 or full blown custom using a BAT, either done properly will shoot extremely well. I think the question you need to ask yourself is which way do YOU want it built and go from there.
Also, if you already have a donor the wait time for your build to be completed will likely be less.