I am a big advocate for the monk class being renamed "pugilist" or something, but dont worry its not like a european monk, or anything like that... even in flavor, and its not that much like an eastern monk either (just a bit).
Monk is just a name.
The problem is pugilist is another title that's a bit to narrow in it's implications. It's basically the same problem as monk, just moved to a different place on the venn diagram.
We need a name that is broader.
The more I think, the more "Mystic" doesn't seem so terrible. Not really a caster, but someone that does weird supernatural stuff, and even base monk has a lot of that.