My 2 Bob's worth.
Alternatives to .303?
.30-30, of course
.30-40 Krag; almost the same overall cartridge length, "standard" .300 / .308 barrel, same HS gauges (give or take) as .303.
.30-303: This is a Hybrid, using ",30 cal Barrels but with a .303 chamber reamer run in. I built one years ago as a "bitsa" bush rifle. It has a 1:12" twist, so is "marginal" at best with long / heavy bullets, but with 155gn SMKs or similar=weight "hunting" bullets it has put a bit of venison on the table.
Then, there are the various Oz and Canadian"wildcats", from .22 up to .358".
Or, the rimmed version of the 6.5 x 54 MS, the Dutch / Romanian 6.5 x 53R (same rim and body sizes as .303.
.
How "feral" do you want to get?
.44 Mag using desert Eagle mags? Again very similar head size to .303.
7.62 x 39 is a good option, BUT. Mini-30 mags are not ideal as the heavy mag spring can cause feed issues; rounds "popping out" during slow feeding, for instance. If you are handy at spring-winding, maybe.....
Better alternative id the single-stack 5 rounder for the CZ 527 bolt action. Less feed drag and easier ti work up an adapter for it.
HOWEVER, if you have an "un-bubba-ed" No1 Mk1 action, including the correct pattern of bolt and bolt head, consider a "functional "recreation" in a calibre from the above list. There must still be a few of the appropriate nosecaps and rear-sights still floating about. I have owned several of the "correct" components, (Nose caps, bolts and bolt-heads, etc, over the years, but as I was unlikely in my lifetime to ever see the rest of one for a sane price, I have traded or sold them.