The fundamental problem with 4-drive-wide rackmount gear is that there is a need to cool the drives. This happens by sucking, hard, to force air through the tiny gaps that exist around the drives in the drive bays. Causing this static pressure differential is a process that consumes a lot of energy and that translates to noise. The fans that are used are beefy, industrial grade fans that are tolerant of such abuse and will still last a decade or more given such abuse.
Your problem is tougher because of 1U; the little 40MM fans are incredibly noisy due to the physics of it all.
A better solution for you might be to go for a Supermicro SC826 style chassis, 2U x 12 bays, specifically with the PWS-920P-SQ ("super quiet") power supplies.
A lot of people buy these and then try to toss Noctua fans in with 12 drives to keep the noise down and maximize the storage. Don't do this, it's dangerous and stupid. You will end up with a nice little oven up front, especially as the fans fail, because the Noctuas are not designed to generate
a high pressure differential. Stacking two drives on top of each other creates a hot spot between them, and if you do not have the "oomph" to forcibly move some air through the gap, it gets hot. Twelve of them is a recipe for disaster. The two drives in the middle especially have nowhere for their heat to go, despite the irony of having some fans directly behind them. If the fans cannot move significant air, the drives just warm up and bake at far too high a temperature.
But what you *can* do is to remove every other drive in a checkerboard pattern. This gives you capacity for six drives, no two drives adjacent, and six slots for air to easily flow through, so then you can use silent "gamer" fans in place of the industrial fans on the bulkhead. The drives will run a slight bit warmer, but because there is a way for heat to bleed off, it's generally possible to get this working fairly quietly.
It is also possible to do this with eight drives by leaving the middle row empty.