Jags, your proposed route looks ok to me, the main thing is to avoid the A75.
The A712 which you have on your route between Newton Stewart and New Galloway shouldn't be too bad, the rest of the route is on minor roads which should be nice and quiet.
An alternative, but longer route would be to follow the National Cycle Network routes, NCN 73 from Stranraer to Newton Stewart then NCN 7 from there to Dumfries (you would cut off before Dumfries though, to get to Barnsoul).
See
https://www.opencyclemap.org/ for these routes.
Following NCN routes can often be a bit infuriating though, unless you have it programmed into a gps device telling you where to go at junctions.