Q: When you have a character with a long monolouge and you want to break up the paragraphs, where/how do the quotations go?

A: When you have the paragraph change, don’t put end quoations on the last sentence of the paragraph, but do put starting quotations on the beginning of the next paragraph:
AAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAA.AAAAAAAAAAAAAAAAA.AAAAAAAAAAAAA.AAAAAAAAAAAAAA.(NO QUOTATIONS HERE).
AAAAAAAAAAAAA.AAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAAAAAA.AAAAAAAAAAAA.AAAAAAAAAAAAAAAAAAAA.AAAAAAAAAAAAAA.