Instant move option?

No, unfortunately there is no such option or mod. This is a well known issue especially once you get later into the game.

  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.

Actually, another method is to turn off all auto go-to options, and then zoom far enough that scrolling to the edge makes everything disappear.

That almost completely removes any graphic processing to do.  Turn processing is pretty much insta-click no matter how big the game is.  It can be mildly tedious depending on how much you micromanage your empire, but it really helps on the turn processing.

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.

You can press 5 to zoom out to tactical view.  1 through 4 zoom you in to different angles.