Well, I've had a reply from NYMR - it simply says that bicycles or tricycles can be carried, in the guards van, subject to space being available, at a cost of £2. (it looked like a bit of a cut and paste answer to me). So I guess that's a yes then. If there are many of us, we just make sure we're at the station early enough to beat any other prospective cycling passengers to the van.
I did ask if I needed to make a reservation, but they haven't said anything specific, so I assume it's ok to just buy a ticket on the day. I know it's Goth weekend - are Goths likely to be inundating the local steam railway? Or is 'Goth'/'Steam Enthusiast' one of those Venn diagrams with very little overlap?