In the meantime, I'm trying keep the site running, prioritizing scheduled tasks as much as possible without breaking things and attempting different approaches to try and help the site run smoother. Can't say for sure that there's progress but it feels as if the site is just a tad bit more stable.
It does feel faster today.
Is there a chance that this experience will help you run the site easier in the future, if replacing the part solves the current issue? I mean, while trying these solutions now when you need them, maybe you learned something that will be useful later. At least I hope so.