Hello and Welcome

Well you have established that you are enthusiastic and have also had experience in teaching (in a in-direct manner), which will go well when applying and in an Interview.

Possibly look into doing a TEFL or similar English program? While although you will have your degree, having a TEFL cert or similar will be advantageous. It shows that you have at least learned or experienced teaching English. Although applying for the JET program a TEFL cert or similar isn't actually needed (but it's still advantageous).

Iv heard, although speculation, from someone I know that having a drivers licence is also good to have. It shows that you can be flexible or being able to move around freely and teach in multiple schools. Also if there is a job in a school in an area where there is little public transport, it shows you can travel.

Again, you have expressed interest in the culture which is also good. They want to know that you are genuinely interested in Japanese Culture & language as a whole so you can better experience your work and also provide a better work ethic for your students.

I can't really provide much more info myself, I don't have the experience in doing any of it myself. Just hear say from friends and from looking up information. I think trying to get as much experience (perhaps teaching private English lessons?), you may be able to get references from doing so as well which always aid an application.