Hi -
If you decide to ride up to Mt Rushmore, be advised that the folks at Rabbit Cyclery might be convinced to hold your excess baggage so your trip can be unloaded. They also had a restroom/shower facility in the shop. Their website indicates a 'barn' for overnight accommodations. They had a well stocked shop and though I didn't need to use it, a good repair shop.
I managed to include the Mickelson Trail on a cross country tour last year and I'm glad I did. At times I felt really remote. The entire trail (north to south) wasn't completed by me - I detoured to Wind Cave Park and stopped in Hot Springs for a swim/soak.
We are your "experts" on the Mickelson Trail for Rentals & Shuttle Service in the Black Hills