Two alternative options. They won't help with power consumption, but might with noise.
Enclosure
Are you willing to just put an enclosure around the NAS? It's an approach that I was looking at a while back. Surprisingly, there doesn't seem to be much by way of inexpensive, readily-available acoustic enclosures (at least not large enough for a whole mid-tower PC, which is what I cared about...maybe a NAS might be more-doable). It's not rocket science if you're willing to put time in to make one, though.
https://www.youtube.com/watch?v=HMU4V2S-feM
Like, get drywall (cheap, heavy, good for blocking sound). Cut drywall. Glue/nail drywall pieces into shape of box. Cut hole in drywall for in/out fan. Put fans in holes. Use foam sealant to close off cracks. Line interior of drywall with acoustic foam (good for absorbing sound). Put enclosure over NAS, turn on fans.
You might be able to even put tubing around the inflow and outtake if that isn't sufficient; if a computer-style fan isn't enough, it's possible to get variable-speed flex-duct inline fans in quieted housings capable of creating some air pressure, forcing air down the thing, stuff like this.
Just move it
If you wanted something like a USB enclosure, then you'd have some distance restrictions. But you're talking about a NAS, so it's on Ethernet. Ethernet is pretty easy to run about as far as you're going to reasonably want. Just find some location that isn't near anyone and has access to power and where you can get Ethernet to.