H&R rifles

[H4831]

isn't the 303 with .308" bullets essentially the 30-40 krag?

Certainly very similar. Krag is shorter in the body, base to shoulder, but has a much longer neck, making the case longer than the 303. Rims would appear to interchange.
Here they are, Krag on the bottom.

 

[Calum]

I realize that there's the whole controversy between .308 and .311 bores (which I think is mostly rubbish, having shot, without incident, lots of hot loaded .312 bullets in my old Ruger mini-30 with a .309-ish bore) -- but otherwise, my pea brain thinks it would be a pretty do-able project.

Use the right bullet dia with the right bore dia.