If you anons really want to do JET, you need to realize the weebs in charge really don't care about teaching experience, desire for teaching, or suitability for teaching. They see it as bringing cultures together. The successful JET applicants talk about how much they love Japanese culture and how they want to do shit like start an English speaking tennis club for grannies in whatever inaka town they get sent to.
The whole purpose of JET is to send gaijin to the countryside. Most gaijin don't want to go to the countryside unless they want the cultural and language immersion. Gaijin with teaching experience can get jobs in the cities, or even worse, cause friction with the Japanese schools and teachers you're supposed to be acting as a human tape recorder for. If you appear to be a candidate who could piss of the Japanese teachers, or fuck off and take your work visa to get a better job in a more exciting city, you'll face an uphill battle convincing them to pick you.
They think they know from their own experience that the best JETs are weebish human tape recorders. So be that guy. Tell them you want to immerse yourself in Japanese culture and language and downplay any teaching experience you have. Don't hide it, just use it to demonstrate that you're not afraid of kids and you can follow instructions.