I'm not saying your bikes don't work Junkyard, although there's a vast degree of subjectivity involved with 'works', but to recommend people mix and match chains cassettes and shifters is pretty daft. It will just not yield satisfactory results in the vast majority of cases.
There are some exceptions, you can use a 10 speed chain on a 9 speed drivetrain, it will wear quicker, but the weight weenies like doing it.
A 7 speed chain/cassette will more or less work with an 8 speed shifter as the gaps are identical, the chain is the same 7-8 speed, but the 8 speed cassette is wider. 8/9 will not work, as the cassettes are the same overall width, with the 9 speed sprockets closer, an 8 speed shifter will constantly overshift. Whatever you say.