However, I recently reformatted my PC, so the drive that had Steam on it is wiped clean. This worked dozens of times without issue. In some cases I moved games back to the SSD from the HDD if I wanted to play them months later.

When I finished the game, I used SM to move it to my HDD to free up SSD space. I'm familiar with Steam Mover from having my Steam Install on my SSD that also had the OS on it.