My question is...
Do I need to be doing some kind of file system maintenance with this?
Should I be running fstrim or some other utility on occasion?
You're welcome, I've got another update I'm getting ready to push here to help deal with some of the YouTube API changes that recently went into effect that have taken out some of the automation I've been able to enjoy with it.
As far as the stuttering issue, and file system maintenance. If you're running Rasbian or another Pi oriented distro on it, I don't think file system maintenance should be needed. I've easily got a dozen Pi's running around the house and the office, and I've never encountered a need for that. (anecdotal information at best as that may be) The scripts as written shouldn't be writing many files to the filesystem.
Are you running this on a RPi4 or one of the older models? I'm not certain how well this would run on the older pis (it should be okay I'm streaming from my 3D printer on a Pi3 while also running Octoprint, but I haven't tested this specific setup on anything other than a RPi4). If you're monitoring the stream I'd take a look at htop and see what the CPU utilization is looking like, usually the stuttering means you're not able to transcode the stream fast enough which on the RPi I've so far only found 2 causes for, 1) you're not using the h264 stream from the camera (you would notice that from the get-go most likely though) or 2) you're maxing out all the cores and there's not enough processing power left. For number 2 I've only had that happen when the RPi starts throttling the CPU because it's overheating (which is likely something you'd see later in the broadcast)
If you want to check the temp on your RPi just issue the following command '/opt/vc/bin/vcgencmd measure_temp' and you'll get the CPU die's current temp out in C. The RPi is going to start soft throttling the CPU when that gets over 60C, and by the time you hit 80C isn't going to be throttling it pretty hard.
I did quite a bit of testing with the broadcasts and cases before I deployed these, hoping I could find a fanless case to use for this, but in my testing it wasn't possible to do an hour long broadcast without having a fan on the system, so if you're using a fanless case, that's probably where I would start.