75" wouldn't work for me. Im about 6'3". My barn ceiling is about the same height as yours. If I can't come up with a way to do something like you did I could always make it a storage space.
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Yeah you would have to rob a couple of inches from the top. Or, you could go with 2 x 6 joists on a closer centre. I used 2 x 8.
I have a couple of inches to spare for headroom, never had a problem except with that damn welding helmet..