I also have a history BA and strongly considered history PhD programs. To me, three graduate degrees seems like an awful lot. If money isnt an issue, or you are lucky enough to have them all funded, then maybe thats not a big deal. It still stands that someone is paying a lot of money for this to happen (either you or the school). If you know you want to get a history PhD then why are you getting two masters first?
I get the Japaneese Studies idea becuase that makes sense in the context of a back-up plan to teaching or as a specalization and additional knowlage if you want to teach courses on Japaneese history. I'm not really sure I see the vision behind the classical civilizations MA though. If it were me, I would want to cut out the extra study and go straight for the PhD, which you absolutely need to teach. I'm pretty sure your PhD reaserch interests will overshadow any MA research when applying for jobs. I see that you mention archeology as well, but if that really is a viable back-up plan then scratch the other degree. One back-up plan is enough, in my opinion.
I'm also really not sure how two unrelated masters will help you get a postion as a professor. The fact that they are unrelated seems to make that awfuly unlikely, considering one wont improve your ability to teach the other. History professors usually have pretty clear research interests.
I don't mean to be negative at all, I guess I just wanted to share my initial thoughts because you asked. I'm not sure getting three degrees because you couldnt chose is really worth the time. I have a feeling one passion will become clear to you later, which will make the other MA kind of a waste of time. That happened to a lot of people I know personally, and they all wish they hadn't rushed into unnessesary school. That time could have been spent improving your understanding one subject or working at a job you love, which is really the ultimate goal of all this school anyway. (obviously the education is an end in itself, but I think most of us would agree that we eventually want to move past that as well.)