Sarg, because those barrels look like they were originally bored and chambered for the 303, and then later altered to 400-360NE, would mean that a really careful measurement of both the bore and groove should be taken, as well as chamber dimensions.

I wouldn't be too concerned if it turns out to be a .358 groove as that should allow you to use 400-350NE cartridge cases and loads.
I've been shooting a 400-350NE for close to 20 years, and it is a great little cartridge.
You have a wide variety of bullets available including the wonderful Woodleigh 310 gn softs and solids.

Double check the bore, groove, and chamber measurements before doing anything else would be my advice.