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Would a Zav be allowed to have relations with his wife while she is Tahor? I can't think of any source to forbid it.
Yep. See Tosefta Zavim 1:9, זב מותר בתשמיש המטה בימי גמרו, and Chasdei David there. Also Yerushalmi Shabbos 1:3, לא יאכל הזב עם הזבה הא זב עם מצורעת מותר, and Pnei Moshe there.