Non-native English teaching - the visa

I know this question has been raised many times, however I'd appreciate any and all insight into my specific situation from anyone with experience:

- I'm from Croatia and have a masters degree in journalism.
- My command of English is excellent in all aspects
- I have a slight vague European accent, but nothing that would impede anyone from understanding me, and certainly nothing nearly as strong as many Indian English accents around
- I have no teaching experience
- I have had English classes as part of my formal education for 13 years, but I have never had ALL education in English, nor have I had any education outside of Croatia
- I have attaind a Cambridge CPE certificate of proficiency in English, the highest possible level in that series
- I plan on getting a TEFL/TESOL certificate before trying to get a teaching job in Japan
- I understand only very very basic Japanese, but learn very fast (spent 5 weeks there last year, could communicate my basic needs by week 3 with minimal effort put into learning it)
- Being from Croatia, the working holiday thing does not apply to me

I understand that the main obstacle is getting a work visa, do you think the CPE certificate and TEFL/SOL would be of help there?

I've read and heard about people from many non-English speaking countries teaching in Japan, though often that getting the visa was a pain and involved some former employers and whatnot vouching for them. I've been told about people from France or even Croatia as well teaching English in Japan for years.

Also I'd *really* want to work as an ALT, for which it's supposedly harder to get the instructor visa than the humanities visa for eikaiwa.

I'm just trying to make this happen and have been planning for a few months now (I'd likely go in early spring 2016) but have only recently found out about this obstacle - until now I was under the impression that if you get a job - you get a visa automatically via employer, regardless of country of origin.

Most importantly, is there ANYTHING else that would increase my chances of getting the visa/job?

There are three types of "teacher" visa: "Professor" for teaching at universities, "Instructor" for teaching at elementary, middle and high schools, and "Specialist in Humanities" for everything else. Of the three, "Instructor" is the only one which requires having received 12 years of education in the language you want to teach, so that's probably out of the question for you.

If you really want to work in an elementary, middle or high school, you have to get another visa, the most plausible option being a "spouse visa" or permanent residency if you stay long enough.

All this is only for visas, others will be able to answer regarding job offers.