To add to the diagnostics of this, I watched the transcode files closely while this was happening (this only happens on my android phones - all other devices work flawlessly such as Roku and Chrome).
There are two transcode folders that get created - one is for (im assuming) receiving the .ts files from the HomeRun, and the other is to transcode to the appropriate quality for pushing to the viewing device. I can predict exactly when the stuttering starts to happen and that is when the total amount of files in the folder that is pushing to a viewing device reaches 300 parts. That seems to be the limit of some process where the oldest files in the directory start getting deleted, but I dont know if that is related or not.
Can anyone else confirm if when 300 parts (or files) are reached in the transcode directory that this happens to them as well?