Great question — answering as the UphillTech team:
The fan cover should give you a fair bit of flexibility in ceiling thickness, so you really have two options. Either glue something like a plastic frame over the hole with a cutout for the new fan, or repair the drywall. I don't consider a drywall repair like this challenging, and I don't like non-standard solutions unless necessary, so that's the way I would go. I don't know of any ready-made plastic frames, so you'd have to buy a sheet and cut it using carpentry techniques. How you fill the gaps with drywall depends on the backing situation. You can simply screw some strips of 1/2" plywood to the existing drywall and glue in some strips of drywall, or even just more of the plywood, or you...
Full answer by isherwood: https://diy.stackexchange.com/a/329931 (CC BY-SA 4.0).
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