1) steam will not rediscover the files automatically at startup or by attempt to launch the game, nor is there any specific option
2) the existing file discovery process is instantiated by forcing a new download of the game
3) this process will not begin unless there is enough free space for the game
So in the end, I had to copy the files back to the HDD to make space on the SSD, start an install of the game on the ssd, exit steam, copy the files to the SSD again, open steam and resume download, then wait for it to verify each file.
If you have a second hard drive (or maybe network drive, haven't tried) you can also create a steam library folder on that drive and just move the game to that library from within steam. That way it will still get updated.