Its mainly noticeable as a unstable framerate independent from any real system load. The Latency of your internet connection is the actually deciding factor while the game is waiting for the cloud save to update.

The issues you describe sounds very much like the consequences of packet loss somewhere between the host and the clients. Anyone using mobile internet or WiFi instead of all cables? Thats the main culprit for these problems - their net code never was super stable and badly coped with spotty connections.