.404 Jeffery will fit your classic armoury of 6.5x54 and 9.3x62.

It can be loaded to similar to the 10.75x68. Original ballistics were around 2100 fps but now two or three hundred fps are possible with a 400 gr projectile.

I think the .416 Rigby would be too long.

A 9.3x62 is legal in some places.