I have the model you just sent us and again I cannot duplicate the behavior you describe. Your model takes less than two seconds to Auto Save. The user interface is locked for less than two seconds. I am running on 10.11.5 with the 3DConnection 10.3.1 driver. I have tried both the SpaceNavigator and the SpaceMouse Wireless. These are the only two 3DConnexion devices we support. I see you have switched to a SpaceMouse Pro, which we do not support. That may be your problem.
When I measure the Auto Save time, I am using a special build of Rhino that displays to me when an Auto Save starts and when it ends. I would not be able to measure this time otherwise. An Auto Save will never start while you are using the mouse, keyboard, or 3DConnexion SpaceNavigator or SpaceMouse Wireless. An Auto Save might start if all of these devices are idle for at least 15 seconds, but there is no way to know when an Auto Save starts (and ends) unless you have a special build of Rhino.
You say that Rhino stalls for 7-10 seconds. How do you determine this?