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Something else you could do which would probably be easier, if you have a planer, make a 1/2" furring strip, then 7/8 then a 1.5" board and run them the opposite way the joists run. It looks like you have about a 10 -12' span and the added pitch would increase drainage. Before you add the ceiling, use treated wood cleaner and then seal the joists using a pump sprayer.
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Nick
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