Can't get right sized through wall unit
I'm building a 165 sqft shed workshop better than my house, with closed cell foam insulated finished walls and under roof, energy star casement window and energy star french doors, white PVDA coated metal roof. Location: San Antonio, Texas.
The problem is it's not easy to get a right sized fully featured through wall air conditioner that's not considerably oversized. I figure 5000 cooling BTU would be more than enough, especially for keeping building within economical wide range (65 to 82 degrees) when not occupied, as it will be mostly, but mainly for protecting the contents from damage, which is actually my main concern for climate control, since I largely imagine using this room during evenings and nights and opening the doors and window then anyway.
But through wall air conditioners typically start around 6700 BTU, and in order to get integrated heat one usually has to go even higher, 8350 in one brand and 9700 in another that looks nicer. It would be nice to have integrated heat on the built-in digital thermostat and timer, and one brand even offers that with a circulation mode, but that's 9700 cooling BTU minimum. I'm not sure about the availability of split units as low as 1/2 ton, but anyway a split unit seems like far more expense and complication than needed.
Is there any way that room air conditioners can be downsized for more efficient operation? Have I overlooked some obvious options? Am I making a mountain out of a molehill?