The language school allows me to file for the PT work permit.
So my initial question is it possible for GEOS AEON etc hire someone Part Time given that they do not have to go through immigration for me?
Yes. The special permission allows you to work at practically any job. If I understand correctly, though, you cannot ask for that permission unless you actually have a willing employer ready to provide the work. So, you'd have to explain that to GEOS or AEON. I don't know if they hire such types of people, and right now Japan is flooded with teachers.
Or should I try a conversation school?
Uh, GEOS and AEON
are conversation schools. Big ones with hundreds of branches.
Secondly, I know you can get an ESL job in Japan with three years teaching experience. ( i dont want to hear about how the Degree is the law, it isnt. Or I dont need to read how "hard" it might be as I have read many different opinions on this matter)
How is that verified?
You verify your previous teaching work experience any way you can, whether with tax records, your face in a school catalogue, previous contracts, pay stubs, etc.
( The experience) Obviously if option A works out and I work for a school while on the student Visa I will have over 3 years experience and be close to finishing my BA online.
The 3 years must be full-time, please realize. So, for example, if you work half-time hours, you'd need to be on that student visa 6 years.
But if it does not, I know I am allowed to take private students with the permit as I have already asked but would this count as teaching experience?
What exactly was explained to you? Private lessons are private contracts that really cannot guarantee any sort of work hours or pay. That's why, for instance, you cannot self-sponsor with private lessons. I would also think that private lessons, unless you have your own formal school, would not count as teaching experience per se. A good lawyer might be able to finagle something out of them, but I wouldn't count on it.
You seem to be in a bit of a hurry to get that visa. Why?
Other options to live and work in Japan are pretty limited. Cultural activities visa lets you study a craft under a master, but you need to have done some studying on your own beforehand, I think. (martial arts, bonsai, pottery making, indigo dyeing, sword making, etc.). It also lets you do PT work with the same special permission. No other options unless you qualify for a working holiday visa (Americans don't), dependent visa, spouse visa, or SOFA status, or unless you have sufficient (usually 5-10 years) experience in another type of career for a different work visa.