I think you may not understand that this is not a 'train trip' to get from point to point . . . it is a wonderful wee excursion train and you will see a a lot and have great photo ops. You don't need to ride the entire route -- do a segment, get off at which ever station you decide and it is timed that you can catch a return train to your starting point without much of a wait. Especially with you being in Rye that long you can easily fit it in . . .

Train Photos - SAMSON- Romney Hythe and Dymchurch Railway

ipernity: Tractacus' photos with the Romney Hythe & Dymchurch Railway

Sorry, I think I would rathertake a photo of it than be in it :)

wrenwood, I'm glad you've got a good chunk of time in Rye - you will love it I'm sure.

They aren't everyone's tasse de the but do you know the Mapp and Lucia books by EF Benson? You might enjoy them.

https://www.goodreads.com/book/show/60079.Queen_Lucia [the latter books are set in "Tilling" aka Rye]

They have been televised but even better they were serialised on BBC radio 4.