The dharma found in books isn't nearly as dynamic as the dharma found in communities with other teachers and practitioners. Which sounds like what you are looking for if you are looking for a monastery
May I make a suggestion? Have you considered visiting a temple in the US, make a connection with a teacher and pursue a priest-path first? You can then live and regulate your life as a monk until you are fluent enough to move to a monastery in Japan and you develop connections to overseas Koyasan through the temple and your teacher. It would be more gradual and you'd have people who speak your language, teach you and guide you in the practices while you learn. On top of that you'd have the connections and community in the US with more similar cultural understanding to your own perhaps. You can easily call or email one of them temples and discuss your interest or plans and they can advise you as well. That is free and doesn't require travel yet!
Either way...there are quite a few people in the US you might want to contact or meet with when you can. Discussing with them and then training under them in some form either occasionally or residentially if they have that available. If you want to become a Shingon monk finding a teacher you connect with and who would accept you as their student may be a first priority.
Below is an open daily service for lay practitioners that is available that does not require initiation- though you'd be missing out on pronunciation of the mantras, tone and chanting style that you would learn if you were connected with a temple. It is more to give you an example of a daily service a lay person may do at home. So if you learned this you may have to relearn it based on however your temple does it in the future. If you call or visit one you can also ask them what an appropriate daily practice would be for you and your current situation.http://www.shingon.org/ritual/daily.html
You can also simply chant the heart sutra everyday (even a few times if you want) and memorize it in Japanese. That is a mostly universal practice in in the forms of Buddhism from Japan.
I don't know how Shingon monks or priests support themselves. According to academic type literature and the reports of friends who've been to Japan...they mostly support themselves by selling temple services or having a part/full time secular job outside of the temple. Huseng might know more about how Shingon monastics support themselves vs. how the temple-priest situation does...though I imagine it has as much diversity as there are individuals? It is interesting topic always as money and dharma tends to be a difficult issue and they've been doing it in some unique ways in Japan it seems?
You could also try contacting Shinnyo-En (a off shoot of Shingon) and see if that is your jam? http://www.shinnyoenusa.net/
They are a priest organization and really oriented towards lay communities but it could be a beginning step in learning more about Shingon and receiving some guidance and language practice.
Just some ideas...and whatever you decide...good luck to you!