I am in the process of building a 360 Imperial (358) and did some measuring.
The Rum line of cartridges IMO are just the Imperial's with the shoulder pushed out
Like Dan was saying the Imp's and the RUM's are 404 based they are all the same lenght.
The Imp.and Rum have the same body dimensions,the 300 and 375 Rums have a .045" longer datum line .
This is great if you have a Imp. cal.because now you buy Remington bulk brass and run it through you sizing die and presto.

Hope this helps
Regards Martin