Sweeps is definitely the most intense folking experience within range, but the trains are indeed a problem.

There is a seedy guesthouse called the Great Eastern by Strood station (easy walk from Rochester) that real folkies may not have cottoned on to yet, if stopover becomes desirable (or within permitted timescale). Never been in it myself but ot looks really rough from the outside - the sort of "Rooms from £10 per night" thing (might be a bit more)