This answer in not the answer you want.
There are almost certainly more options for a button's appearance than are documented in the Help Center. As far a I know there is no way to discover what appearance options apply to buttons. This seems to be a deliberate policy on the part of WRI.
I recently had a exchange of email with WRI tech suppor on a related matter,
SetterBar. This was their position on that subject:
Many functions like SetterBar have optional arguments
available which are not documented. Typically this is because the options
are not ready to be exposed because we haven't been able to fully test them
or because their behavior isn't fully ready yet. We don't provide any
documentation on them because their behavior is not guaranteed and they may
not be present in a future version of Mathematica. We do not actively
prevent people from using these hidden options however if they find them