A belated response on unmedical and medica.
Unmedical is listed in the Shorter Oxford, so I agree it should be allowed.
It's true that some dictionaries identify materia medica as an assimilated expression, but that does not persuade me that medica (or for that matter materia) should be allowed, because I don't think you could say that either part of the phrase is an English word in its own right.
However, it turns out that medica is also an obsolete (late Middle English to mid-18th century) alternative to medick, the name for various leguminous plants, including lucerne, aka alfalfa. The word is unrelated to medical: the plants were believed by the ancients to have originated in Media - modern-day Iran, more or less. Medick is in the Chihuahua word list.
So, on that basis, medica could make a claim for admission. But I'm still not convinced - an obsolete word used in widely-read works of literature is one thing, but a word you might only encounter in a centuries-old natural history book is quite another.
