Due to light travel time, we observe astronomical objects as they were in the past. If we knew objects' motion (relative to us), it seems like we could extrapolate to their present positions, but I can't remember ever reading about anything like this. Has there been any work like this done--or is there some reason why it would be pointless?
The geometry of space-time is a major issue in cosmology, but the focus is on cosmic time-scales, the data (necessarily) are from the past, and physicists can sometimes get a little testy if you push them to use the word "now" in reference to distant things. But in casual conversation, you can say that the Andromeda Galaxy is "right now" closer to us than it appears (or vice versa for most other galaxies).
But as @Stuart Robbins said in his comment, no information can move faster than the speed of light, so scientific predictions outside the light cone are unlikely to have a practical benefit. (I hesitate to say "pointless" because I'm not a physicist or cosmologist.)
Very interesting and thought provoking question. Unfortunately we are not in the era of "Enterprise" to care that much about the current placement of cosmic bodies further than our Solar System. For the bodies in our Solar System we do map objects' current or predicted locations for various reasons as you are aware of.
To know where an object is 'now', you need to know its space velocity as well as its distance so that you can calculate its present three-dimensional position from the position that you measure from its light. For most stars, it's easiest to get the radial velocity since that just needs a spectrum. To get the velocity perpendicular to the line of sight, you need both its distance and apparent motion in the sky. For distant galaxies, one can't normally determine space velocity at all since the measured redshift is made up of both distance and space velocity effects; and, even if they are moving very fast perpendicular to the line of sight, it will take thousands of years to see this motion on the sky.
So, in short, it's a lot of trouble for very little gain.