Remington built 1903 rifles on the old Rock Island '03 tooling until early 1943, when it was superseded by the 03-A3. A Remington 1903 isn't much different than a R.I.A. 1903, except the later production Remington '03's show significantly more tool marks and aren't finished as well.
Any high-number '03 in good condition would be suitable for a .284 Win. Or a standard magnum, for that matter. Just make sure you don't have one of the old case-hardened bolts (small single gas port).
As JB noted, legendary gunwriter Bob Hagel did indeed build a .284 on an A3 action and wrote it up in the 1965 Gun Digest. Or more correctly, he had the equally legendary Fred Huntington of RCBS put it together. In any event, he discusses throats, bullet seating and various loads in detail. He doesn't mention any feeding issues. Most of the loads Hagel notes in the article are pretty hot, which isn't surprising.
