I'm no expert but I did stay at a XXXXXXX place once.
Belt diameter on a H&H is .532, head diameter on a RUM is .550 difference of .018
Length of both is 2.850 w/o bullet.
Shoulder on the H&H begins at 2.412 and the round is .448 at that point angle is 15 degrees and the shoulder ends at 2.550.
Shoulder on the RUM begins at 2.3873 and is .530 at that point angle is 30 degrees and the shoulder ends at 2.4912.
The issue is where the shoulder begins and ends. You need a reputable gun smith to look at the overall chamber space available since the barrel must come off and be turned and threaded to set it back a bit before rechambering. There must be enough meat left to handle the 65K psi of the RUM safely. A #1 shouldn't pose an issue but I would consult an expert licensed smith.