When I rode in 2014, they stopped both directions at Tall Timbers. Thats because they take folks up there in a special car for Tall Timbers clients, and drop them off in the morning and pick them up again going back to Durango. I don't remember any stop at Tacoma. We did stop at Needleton each way for water, which is why I consider that to be a good area to get off and on later in the afternoon. Elk Park would be another one. If the train stopped in Tacoma one could walk back to the High Bridge, and maybe get the next two trains there, but then its a long wait for the afternoon trains to get you again.
Jerry is right, in the old days they would pick-up hikers anywhere they flagged them along the way. There were few back-backers in the old days. Anyway I still think when they are running peak amount of trains this idea of buying a round-trip ticket and spending time in the canyon somewhere would be rewarding. Since I have never done any photo specials(Aside from the D&RGW days), I personally have never gotten any shots between Tank Creek and the Animas River Bridge in Silverton. When they had those Railfest events, one could have taken a goose from Silverton and gotten off somewhere and done the same general plan, as long as you knew the schedule.
Hard to do this on the C&TS as there is only one train generally in each direction. Driving to the nearest spot and walking is the only solution, or a charter of course.
Greg