Hey lads, same issue here with my RX 570. Game runs agreeably enough most of the time but stutters like you mention.
In the attached image I got a short example of one of the spikes. GPU usage drops right to zero, but CPU shoots straight up for the spike, then they both immediately return to normal. I can't tell if the spikes happen more often when the GPU's rendering a lot of stuff, but it doesn't seem to be affected by it. The spikes just happen whenever.
So far I've tried turning almost all settings down or off. I've turned off volumetric raymarch resolution, which everyone says is really intensive. I've tried a bunch of other fixes from the compatibility menu too, put the game up to high priority and tried running it as an admin. Still broken, though.
