The measurements I found for the Flanged are are virtually the same as posted.

I do find some differences in the HH, but I'm not sure the are significant. The HH has a 15 degree shoulder for one thing.

The comparison of measurement of the head diameter is not relevant from belted to flanged as they are measured at two different locations. The belted is measured at .220 from the datum line and the flange is measured .060 from the datum line. Now I suppose If I did the math and projected the angle so they were in the same spot the difference would still be insignificant.

An alternative not mentioned was to simply bush the chamber to remove the belt but leave the H&H rim. Then turn the belts off H&H cases.

You would have a rifle marked .375 H&H and cases to match that are flanged and not belted also marked .375H&H.