Well, Rigby moved to 43 Sackville in 1912. Guns international had a 400/350 dated 1908 with a serial in the 22xxx range. Speed's book lists serials in your range in the 1922-23 range? (If I read the info correctly, page 225.). But i think the numbering can be chaotic. Others here will know more precisely.

If I was about to inherit a Rigby 350, I would drive to see it and photograph it if I lived on the moon. Surely someone can take some cell phone pictures of it In this day and age.