Interesting experiment with the "rimless" .303.
I saw a couple built on P-14 rifles and using M-17 bolts and some magazine components, many years ago. The sages at the time of this "fashion" reckoned the old SMLE was not up to the task of stiff loads in this modified cartridge; more likely they would simply not feed from the magazine reliably nor extract consistently because of the altered case geometry.
History repeats.
Back in the 1950s, here in Oz, there was an abundance of .303 ammo AND "souvenired" rifles from all sorts of interesting places.
A moderately popular conversion was done to Jap. Type 99 7.7 rifles which, conveniently, use the same (roughly) bore dimensions as .303.
Two approaches:
1. Open out the bolt face for the .303 rim, sleeve the chamber and cut a new .303 shaped chamber. Crude, and feed from the mag was "marginal".
2. Get a bit "Gucci" and turn the case heads down to "rimless" dimensions to more-or-less match the 7.7 bolt face and sleeve / recut the chamber as before.
Had an uncle with a specimen of version 1, even fired it with a bunch of FN .303 ball ammo. Mostly functional, but a bit long in its original trim to be a handy-dandy "farm gun", which is what he used it for. I guess he reckoned that, having relieved some unfortunate Japanesesoldier of his burden, he may as well tuck it in his big box of military engineering equipment, along with sundry bayonets and a couple of 6.5 Jap carbines, and see if he could get his "momentos" home: he did.
I heartily concur that the relatively tiny .303 shoulder is adequate for "headspacing". The problems arise because of "variations", (some of them "after-market" / "custom"), in the chamber dimensions.
If you can arrange for your cases to "fire-form" ONCE to a specific chamber and to then NOT over-work them by full-length sizing back to CIP / SAAMI / "Mil" spec, you will extract greater life from the increasingly expensive brass.
Of course, this approach may mean having distinctly separate ammo for each of several .303 rifles. Not a huge challenge for the organized person.