In the main map screen,  zoom out until everything (ships  planets,  starbases,  etc.) are displayed as icons.  Ships battles and moves occur much more quickly.  Zoom in again at the start of the next turn.  The zoom level at which this happens can be set in the options.

  Sometimes I play zoomed out for a whole game because some ships (nothing special about them,  but they usually all belong to one race) slow everything down when they are on the screen.

You don't have to scroll to the edges. If you fully zoom in on the planet/ship you want to handle first next turn, you still do get a bit of lag as ships enter or move through the screen area, but most of the galaxy still gets handled invisibly. 

Zooming in and out, though, became almost as tedious as watching ships move. Most of the time I'll have some ships with movement points left over, so I process those at that time.