Been slowly working my way through War & Faith.* Yes, Honganji can indeed field a lot of cavalry. One, perhaps exaggerated, source credits them with 7,000 in 1525 (p.162).
* Slow mainly because it keeps launching me into internet rabbit holes to find more details on particular items which involves a lot of back and forth between wikipedia, google translate, and armed with Japanese keywords to ja.wikipedia for more detailed info and finding more Japanese keywords and then searching for Japanese web pages.
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