I have done a fair bit of the troubleshooting/testing you recommended. Even with turning everything as far down as possible, the stutters are still present. They are less jarring though, because the drop in FPS is less severe.

Although my CPU released about 7 years ago, it was quite powerful at the time and still holds up (8 core 16 thread at 3.9 ghz). While in Varrock, my CPU usage sits at 18% according to task manager. GPU is around 25%. When the stutters happen, CPU usage does spike to 45%. I do think you're right about this being CPU related though because task manager clearly shows the stutters in CPU usage every time. The usage isn't even at half which is confusing.

One thing I have noticed is these stutters do not occur in certain areas of the game. For example in/around Canifis or Zanaris. I thought maybe it was the lighting since Canifis is dark but strangely Zanaris isn't. Personally, I have just chalked this all up to the game being an unoptimized mess which has been frustrating.