Perhaps remodelling the future doesn't need to be a Real-Time operation. Perhaps it sits on a lower thread, processing the changes to the model, and the player would have a meter indicating how 'caught up' they were in the time shifts happening. then in front of their eyes, see the changes unfold piece by piece. Once the model has determined that a car should be at position 2 instead of position 1, Instead of just 'snapping' into position, it could set some kind of gravity like pull that visually shifts it into place.
Only the characters interacting with multiple times notice the changes. Everyone else is oblivious. You could get away with larger more interactive worlds this way. You could even process time travel the same way, so when you jump into the future by ten minutes, you see things shift around you until you are settled in your new time. Could make for some great visuals.