The various 2.75” 360s as well as the 400/350 Rigby have a base diameter of .470” and the 400 Purdey has a base of .369” so I guess the 360s could be made from 400 brass. The 400 being 3” cannot be made from the 360s of course.
The 400/350 was introduced in 1899 and the 360 in 1900 and the 400 in about 1905.

Cartridges of the World says they were based on the 400 Purdey but I don’t see how that is possible chronologically.