What I would like does not seem to exist or there are numerous complaints. Perhaps I am not thinking clearly or it is hopeless.
I am searching for a larger mid-tower case that has four 5.25" bays, accommodates six internal 3.5" hard drives, and has some space here and there to squeeze in 3-4 unmounted SSDs. Obviously the case needs decent airflow, but nothing excessive and should be reasonably quiet. At least three of the 3.5" drives need air cooling. All of the fans should be relatively straightforward to replace with typical 3-speed or otherwise manually adjustable varieties. I don't have any use for the clear plastic windows, but can cover them with aluminum foil if needed. Likewise I'm not a proponent of the case side fans. Usually I take them off and leave the grille open.
My current case is about 21" H x 8" W x 19" D. Anything taller than 23" will become a liability as the case is under a table and anything deeper than about 22" will place the mass of cables uncomfortably close to the wall. Case width does not present a space limitation, and I actually prefer a wide case to accept a large CPU cooler. The case should not be insanely heavy either. Usually I lay it on the side to open and work on it in place.