If you are starting from scratch, it is no big deal to do a ".303" barrel on a ".30" blank. The .003" difference is only a minor quibble, especially as it is a three thou TIGHTNESS, not LOOSENESS.
I have done a couple using slightly "tired" heavy 7.62 target rifle barrels. You know the ones: the driver can't get eight of ten "centres" / "V" bulls two weeks in a row and decides to get a new barrel! The biggest problem is getting one long enough as you have to chop off almost the entire 7.62 chamber to get to fresh meat to support the .303 chamber. If you are building a Carbine or "bush" rifle, no worries, but that 25" plus No. 4 barrel is a squeeze.
If your gun-plumber has a .303 reamer with a removable pilot, all he needs to do is swap in a .299" pilot. Going the whole hog, he can also grind the leade-cutter section of the reamer a little more steeply. That way, The chamber will still accept Mk7 ball, if you can find any, as well as a lot of other projectiles. It might make the bench-resters cringe, but this rifle was never intended to be a bench queen, but a functional "service" rifle. I nailed a very nice red deer with the old girl using the 155 Palma bullet. Mind you the range was VERY short: the silly hat-rack was almost about to walk over me as I hid behind a two-inch diameter sapling. I had been using the Palmas for a training shoot with my son and that was the only ammo to hand as we wandered back down the dry creek bed that afternoon. Heart, lungs and liver were "wrecked" by that bullet. Delete endless wild goat recipes; insert endless venison recipes!
The "creative" tooling was used to cut the chamber in my "rough" No4. It works very well with any decent .308" diameter bullet, especially Sierra Palma 155s and a couple of brands of 168gn beasties. It means I can use the same range of bullets in that ".303" as my .308 and 7.5 Swiss.
I whacked a bunch of Yugoball with .311" diameter bullets through that hybrid chamber as soon as possible after getting it together. Pressure problems? None noticed then or any time in the last decade or more.
Despite being 1:12" twist, it is seems to just stabilise the relatively long Mk7 / 8 bullets, but won't stabilise any of the long, extra slinky "VLD" bullets, especially at safe ".303" velocities, but that was never the intention.