Eikaiwas also don't like experienced/qualified teachers, because they are less likely to put up with shady managers.
A couple sites you should take a look at before trying to get into one:
Let's Japan.org | Debunking Eikaiwa and Ramblings in Japan
Dave's ESL Cafe
GTJ - What sort of visa do you have now / can you get a hold of a working holiday visa? I think they are quicker to obtain, although you can only work part-time on them.
You could always, you know, have a shotgun wedding and get a spousal visa
