The Representative who installed my Eaton compressor told me that the way to quiet it down considerably was to route the air intake out of the area. Since mine has 3 air intakes I would probably need to make some sort of a manifold to do this, but haven't done it yet. My compressor isn't objectionably loud. My neighbor has an oil less compressor in his barn and I can hear it running when I'm in my house with his barn doors/windows closed and my house windows closed.
According to a smartphone decibel app ( unsure of accuracy but on a relative basis ) my compressor ran at 142 decibels. Deafening and hearing damage zone. I installed a round walker car muffler on the intake. I used a 1.5" conduit elbow & made a adapter to mount it to the compressor head. Mounted a filter on the end of it. Ran the decibel app again and dropped it to 65 . Majority of the noise comes from the intake. That insulated box is going to cause trouble.
Is the intake a big pipe thread? If so There are some very effective silencers available. Basically needs to be big volume ( 10 X piston displacement ) to soften the intake pulses fed by a tube/port leading from atmosphere . https://encrypted-tbn0.gstatic.com/...j_jzBknzgFkLtNEU8Q12sm9FKTULWz9r6qjlPyBvDNzBj
Or you can buy a used Quincy. I picked mine up for a couple hundred. It's a 1942 308 and you can stand right next to it wile on the phone if needed. It's about 15 cfm at 90 psi and is a continuous duty pump and is ran off of a 2hp motor so it don't take much power to run. Mine is mounted next to my a/c unit outside and the a/c is louder.
Another reason to put it in a safe enclosure or outside is the threat of explosion.... A rusty tank or a sticky cutout switch is all it takes.... Not super common- but a catastrophic event if it happens at your shop.. It really needs to be enclosed more for that reason than noise. I saw a 20 gallon /small one blow one time and it was like a dynomite sounding explosing and it blew the 10 by 10 heavy sliding door and the compressor pump completely across the street as a result....so a 60 or 80 gallon bomb would be unreal I am sure....