Remington 700 action is 1.35" in diameter.
The barrel that's on mine is 1.35" to the muzzle, and is 30". No problem. At 10.5 lbs it might be better to put it in a block just so bedding survives longer with the big 30-338 Lapua, so that's what it will get put in. Shoots very well as is, in the *** plastic stock I hogged out to fit it in.
That said, I'd go 1.25" straight tube for 30" and no block, longer if it was tapered. How much longer would depend on its weight though. My brothers 32" 338/378, well 34" with the brake, but his is tapered to .900" at the muzzle.
It's much easier if you don't use a block and stay below 1.25" too, I will say that.
1.25" and a bbl block still will make stock selection easier too. Get any larger and choices on stocks become quite limited.
Think out the balance issue too, straight tubes is heavy, plan on adding quite a bit to the butt the heavier it gets. Mine'll flip right off the rest the way it is with the light weight plastic stock and no weight. It's so unbalanced it ain't funny! Balance point is about 1/2" behind where the sling stud used to be, so...
This 36" bbl on my brothers Ruger #1 tapers to about 1" at the muzzle. Starts out at 2.002". Barrel tennon on it's about the same length and dia.
Plan on a block if you go 1.5".