I did most the trail in June. From the Englewood trail head to Edgemont.
There is a shuttle service based in Hill City. (There may be others.) I met a couple who used it for a ride from Custer north to a point above Rochford. They were planning to ride back to Custer but got soaked in a storm and got a shuttle from Hill City back to Custer. I asked them what the service charged. They declined to give me an exact figure, but they did opine that it was expensive. On that note, I highly recommend good foul weather gear. The trail has some elevation and cold rain and hail is a real possibility. The night I stayed in Hill City there was hail up to the size of ping pong balls. When I ran into the couple mentioned above that got caught in the storm coming into hill City, the husband's hands were literally blue from the cold as he was not adequately prepared.
Have you looked at the official web site for the trail? I believe there are resources listed there.
Don't think it will be easy to find something between Deadwood and Hill City. That part of the trail is remote. I think there is a bar/restaurant in Rochford. (I stopped briefly at the trail head briefly.) Aside from that, I don't think there is anything unless there is a ranch guest house or two long the way. South of Rochford the trail becomes even more remote. In general, the Mickelson is not a "warm and fuzzy" trail. The surface is rough in places. It's not like the GAP, which is mostly nice crushed limestone. There are some climbs you might not expect to find on a former railroad grade. Ride With GPS shows the climb that starts at the Englewood trail head to be 5 miles with an average grade of 2.8%. I had already done a lot of climbing when I got to that point on the days' ride and was taken by surprise at how hard it was into the wind. South of Rochford, starting at Mystic, there is another climb. Obviously they are not mountains, but if are tired already, they seem tough. Also, south to Hill City there are a ton of bridges. Many of the wooden plank surfaces and not the smoothest. And the transitions between the trail surfaces and the bridges were often bumpy, requiring you to slow down in the exercise of caution. Stopping to open, negotiate and then close the numerous cattle gates can also add time, although maybe not as much without a full load. If it's been wet, it can be very messy and even slower. This year was an incredibly wet year for the Black Hills. The trail suffered damage in several places. At the top of the hill before the run into Edgemont there were short sections of trail surface that had been washed away almost completely. What I am trying to say is that it might take longer than you think to cover your expected daily mileages.
The train from Hill City doesn't go to Rushmore. It goes to Keystone. (Tacky tourist town.) Rushmore is several miles away. If you plan to ride it, be prepared for a climb. it starts out gradual from Keystone then turns into a beast for a bit. RWGPS shows grades in the double digits.
Edgemont is sleepy. There is a park in town which is the official end of the trail. You have to ride on roads to get there as the trail proper ends on the edge of town. I took a rest day there and saw two groups park their vehicles right on the street at the park and head off north on the trail for multi-day rides. If you are really that worried, there is a Sinclair gas station on the end of town that has a large, gravel parking area. They might let you leave your car there. At the end of the trail there is a museum. They may also be able to give you some ideas.
Here is a link to some photos of my trip, which include some from the trail. As you will see, you can see Crazy Horse from the trail. Look left after you cross under Avenue of the Chiefs at the top of the climb out of Hill City.
https://www.flickr.com/photos/105349...57655263744881