.303 into 7.7?

[Sunray]

The Metric designation for the .303 British is 7.7 x 56R. Not interchangable with any Japanese or other cartridge.
"...I've even heard of a .45 ACP round being fired in an '06..." On what planet? The .45 bullet is 143 thou bigger than a .308" bullet.
"...cartridges headspace on the extractor..." No cartridge headspaces on the extractor.
"...so the .303" British will chamber in..." Only because the .303 case is shorter. The bolt will not close. It won't fit in a 7.35 Carcano. Brit case is too big.