Appendix 2 (Engine Symbols: 1921-38) of "The Best Twin" contains the following curious entry:
HE/ 3 1/2 h.p. 1923 T.T. engine ohv, 2,397 x 85mm
If we take 2,397 to mean 2.397 inches or 60.9mm, this engine has a displacement of 495cc. The interesting part is the stroke of 85mm - 3mm longer than the OB. So it looks like the "long stroke 3 1/2 h.p. RA" used a special 85mm crank, with bore the same as the road-going 2 3/4s of the day, at just under 61mm. (The 600 sidecar racing RA, engine prefix GE, is listed as 68 x 82, same stoke as the OB.)
Has an HE prefix motor survived? If you come across a crank that causes the pistons to pop out the top of your OB cylinders by 1.5mm don't throw it away!
Leon