Hi.
How are you today?
I have less time,so this answer is not perfect for you,sorry.
1st
I was at Antaiji few years ago,but I don't know detail at Antaiji now.
But head monk Muho(German) or next head monk Eko(Japanese) answer to you.
Maybe Antaiji don't accept 1 month stay now.But maybe you can ask again,if you
want.
2nd.
I can introduce several temple(monastery).These temples accept long practice stay.
Tosho-ji
Not same temple, Jundo reccomended.Traditional style Zen monastery,lots of monk
from Europe practice here.Adding link in Japanese.
http://www.sotozen-net.or.jp/zazenlist-fo/tosho-ji
Joman-ji
I practiced at here,and head monk Koya(Japanese) can speak English very well,
and monk who came from US stay here.Highly recommeded.
http://jomanji.web.fc2.com/index_e.html
And now I ask several temple.Please wait.
3rd.
As Jundo said,you will not need lots of money to stay,when you can practice at
Zen temple.Maybe need donation,everything depend on you and temple.
Sorry for bad English.And temples I reccomeded are apart from Tokyo for
few hour,but you can use high way bus(Less money need)In city side,
difficult to find temple to Zen practice,as Antaiji.
I will post again.And if you want to ask me,DM or here you can post.
Thank you.
Gassho
Sat today LAH
Kakunen