But I'm reluctant to use both Infuse and Plex for essentially the same thing
Since Infuse doesn't play music, then you need 2 pieces of software anyhow. So what makes you reluctant to use Infuse + Plex? You could set up Plex with just your music library, so the interface would not be cluttered with videos. And, you'd also get the added benefit of playing your music from outside your home (you'd need to buy the iOS Plex app for $5).
I want to do the transcoding on the ATV
If the content is in the format the ATV can play, then Plex would directly play it, so no transcoding needed. Is your music in MP3 format?
A few other options to consider:
1) If you want to relieve your NAS from running Plex, you could put together a $50 Raspberry Pi and use it to run the Plex Server, then just put it onto your network. It essentially would be a stand-alone and sole-purpose device to run the server. Just create a library that is stored on your NAS.
2) I am sure you know this already, but you can AirPlay from your iPhone/iPad. But I assume you want a native TV solution.
3) You could subscribe to Apple Music, match your library to the cloud, and stream from the the ATV's Apple Music app.