Here are the new chamber casts and (below) measurements. Thanks for those instructions Tinker! I am still rounding up lead slugs the right size and a micrometer.

I went to see a knowledgeable gentleman and we looked through his cartridge references, and the only real prospect we could see was the .500/450 No 1 Express, 2 3/4". The part that was contradicting this was the case length being a bit short, but on reflection I may have been measuring a tiny bit back from abutment on the step for the case mouth. Also, the Cartridges of the World measurements are on rounds, not chambers so should have some clearance.

However, those throat diameters are bothering me - .463 to .468 seems excessive over a nominal .458 projectile. Could the throat be larger for the paper patch, or is the lead projectile smaller than .458 for paper patch?

The .303 case is to make me smile, cause this is still an awesome huge round even if it isn't the big 3 1/4" No 2!