A reset will normally change everything, but you can use git stash to pick what you want to keep. As you mentioned, stash doesn't accept a path directly, but it can still be used to keep a specific path with the --keep-index flag. In your example, you would stash the b directory, then reset everything else.
# How to make files a/* reappear without changing b and without recreating a/c?
git add b #add the directory you want to keep
git stash --keep-index #stash anything that isn't added
git reset #unstage the b directory
git stash drop #clean up the stash (optional)
This gets you to a point where the last part of your script will output this:
After checkout:
# On branch master
# Changes not staged for commit:
#
# modified: b/a/ba
#
no changes added to commit (use "git add" and/or "git commit -a")
a/a/aa
a/b/ab
b/a/ba
I believe this was the target result (b remains modified, a/* files are back, a/c is not recreated).
This approach has the added benefit of being very flexible; you can get as fine-grained as you want adding specific files, but not other ones, in a directory.