Your problem isn't OS X. It's each application. Some programs, like iTunes, which famously has its problems, might be more likely to have problems when the external drive or NAS isn't around. Others do better.

For what it's worth, I copied my music collection to Google Play with their uploader. Just barely fit, and had to transcode to high-quality MP3 rather than the original lossless. Still, this makes my full collection available everywhere I go on every device I own, so long as I've got a working network. You might consider something similar to offload the music and save space on the SSD for other things.