The issue I see in all cases would be the GPU sticking out from the mobo.
https://www.amazon.co.uk/Corsair-CC-...s=mini+pc+case
This seems to cover that issue, dropping the height but keeping the width. It's pricey but it's more the idea and dimensions. Which are 39.6 x 25.9 x 32 cm. The PSU goes in the solid white side as you'll understand by looking at the cable management in the images.
Another, see image three, they dropped the width but factored in a large GPU:
https://www.amazon.co.uk/d/Computers...s=mini+pc+case
There's space for two HDD's across the bottom there and should you not need the DVD drive, you could leave the placeholder on and slot a third in there.
Not entirely sure what the smallest would be but I'd rule out slim line cases for the obvious reason, you'd never get the side panel on over the GPU. I think that leaves a cube case.