JR Nakayamadaira Onsen station has nothing.
http://www.jreast.co.jp/estation/station/info.aspx?StationCd=1115JR Naruko Onsen station has nothing but a tourist information counter.
http://www.jreast.co.jp/estation/station/info.aspx?StationCd=1131These are all the four timetable for JR Nakayamadaira Onsen station. I could not find any at 14:40.
http://www.jreast-timetable.jp/1808/timetable/tt1115/1115010.htmlhttp://www.jreast-timetable.jp/1808/timetable/tt1115/1115020.htmlhttp://www.jreast-timetable.jp/1808/timetable/tt1115/1115011.htmlhttp://www.jreast-timetable.jp/1808/timetable/tt1115/1115021.htmlAnyway, this is the timetable for a special Koyo bus for last year. Note it did not run every day. No info yet for this year.
http://www.naruko.gr.jp/file-timetable/bus_momiji.pdfIf you arrived at 14:40 at JR Nakayamadaira, the next bus is at 15:13. You would arrive at Naruko Gorge at 15:18. You would have 42 min to finish the part A before the due time 16:00. The sunset is around 16:50. You may do the green part with this 50 min. If you could take a bus from JR Naruko, you could arrive at Naruko Gorge at 15:03. You gain 15 min more for some viewpoints. So, I think it could be possible.
I think most visitors with a car spend two hours on site. Leisurely tourists would like to take a double time, four hours. To visit all the site shown on the map, a full day. I mean spending a night either at Naruko or Nakayamadaira Onsen. After breakfast, visit the site, walk along, have lunch, walk along, visit Nihon Kokenshikan, Naruko Park and so on. Get back to the Onsen ryokan before getting dark.
Unfortunately, the current Naruko Gorge Promenade is far from complete. Before the heavy rain, the parts A and B were connected. Now in the repair phase. So, I would not follow the above scenario now. But still, I try to visit there around noon. In a sense, its current situation is best to do Naruko Gorge as a day trip from Sendai. 2 hr from Sendai, 4 hr there, and 2 hr back to Sendai. If you could start the day very early, you may consider Matsushima on the return.
The tourist information counter at JR Naruko Onsen might offer luggage storage this year. Do keep an eye on their website. Anyway, you need to get an updated bus timetable from them.