I solved the ffmpeg issue just by acquiring the appropriate ppa from launchpad.net: https://launchpad.net/~jon-severinsson/+archive/ffmpeg
Note that this will remove conflicting dependencies though, so you may wish to go with the above solution from webupd8.org. I also updated to Java8 through webupd8's ppa, which did clear up some issues (but not the noise). However, I found a solution: just change the Audio Files Engines in Transcoding Settings to Audio High Fidelity.
Now I have absolutely no problems with the server; all my subtitles and formats work flawlessly!
One thing to note, however: I am currently working under a Java7 profile, as per the webupd8 instructions for doing so after updating to Java8, because until I experimented with changing the audio plugin, I thought the Java8 update had made things worse. I was probably wrong about that.