Try larger fans running at a slower RPM
This will make things quieter. I am trying to arrange the import of some GMC Noblesse SE cases to the states. These cases have soundproofing throughout the case. All the drives are isolated with rubber and teflon. Even the Power supply is equiped with dampers. makes for a very quiet PC or AmigaOne/Pegasos
Or you can buy ASAKA soundproofing for your case.
The heatsink fan on the Amigaone G4 is anemic to say the least very puny. Not much noise or heat.
But I recomend you replace it with one a little more robust.