Lots of choices if you have the money to spend. Depends also on whether you are sold on the .338 and intend to keep the gun long term? Or are unsure still. Would suck to buy a 5k plus gun then not enjoy shooting it. I tried it before I bought, loved it, and decided on a "buy once, cry once" purchase that I'll have for many years.
I bought a Barrett MRAD in .338, and it's amazing. Have shot it out to 1200 yards on man sized targets. Love the ergonomics and trigger. Also when we go to 700 yards, I just pop in my .308 barrel and same scope, LOP, etc. If that's too pricey, my friend has an Armalite AR-30 .338, and is a 1/3 the price, bare bones gun, but shoots great too.
Hard to go wrong with the more custom guns though for sure.
Never seen a Rem 700 in .338, so can't help you there.