I recently made a screened in porch into a family room and we installed a Mitsubishi heat pump where the compressor is still outside and the cassette with the blower and filter is in the room. It’s kinda like a mini split, but separated into two sections. Anyway, there is a fan setting that is amazingly quiet! Seeing as I hope to be in this home for a while, so I bucked up for the superheat feature, which mostly worked last week when we got down to 4°.
All the best.