It's highly likely you've stripped your bore slug and are therefore seeing only the bore diameter, rather than both bore and groove. Does the slug show clear impressions of the lands like the one at the end of this photo montage? If not, try a different technique and/or raw slug configuration, perhaps as shown here.
How many rifling grooves does your barrel have? If it's an odd number, like 5, then you need to use special technique or tools to get a useful reading.
Measure across the "corners" (red line) for a reasonably accurate reading on odd-grooved rifling.
As for the Remington bullet that measured .3045", were you measuring a loaded bullet just ahead of the case mouth? That might not give you the major diameter, which can normally be measured only after removing the bullet from the case. If you did measure a pulled bullet and found it was that small at it's largest point (usually the back end), then you should recalibrate your caliper and be sure you're employing it correctly. It would be extremely unusual to find a factory .303 Britishprojectile with a major diameter less than .310".