.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.

Information

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[Jim K]

The term "headspace on the extractor" is often used to mean "is held in firing position by the extractor" a different matter altogether. Incredibly, some folks think the .45 ACP cartridge is held for firing by the extractor in a 1911 type pistol. (It actually is when a .45 ACP is fired in a 1911 or Webley 1913 chambered for the .455 Webley auto pistol.)

True, the .303 British is "not interchangeable" with other cartridges but, as pointed out above, the 7.7 Japanese Rimmed and the Italian 7.7 Rimmed ARE the .303 British under other names, at least as far as case dimensions are concerned. But the 7.7 Italian is a lot hotter than the .303 British loading.

Jim