I'm sure it is the rimmed 400/350.
Don't know what "special" means in this case but it would make sense that it would be for the heavier bullet in a single shot imo.
The lighter bullet in the 400/350 is referred to as the 350No.2
Could be that the barrel inscription could read something like "For Rigby's Special (something something) Bullet"
Makers did that kind of thing pretty often.