Being CPU limited is known to cause stutters. To test this, you could either increase your render scale to load up the GPU to the point you become GPU limited, or reduce both LOD’s, traffic, glass cockpit refresh, traffic, and fly a simple prop to unload the CPU and become GPU limited that way as well.
I would certainly upgrade the CPU first in either case here. The 5800x3d was king until the 7000 series x3d’s came out, so expect some uplift with it. Not necessarily increased frame rates depending on your GPU demand, but smoother frame rates. Upgrading the GPU when CPU limited will only get you better looking stutters.