Huh...I'd written this script for a completely different purpose, but it fits here as well as anything else. This GIMP script (JMS-Rhumb.zip) can draw any number of Rhumb Lines from 3 to 360, from nearly any point on the map (10%-90% in the X and Y directions) The map can be just about any size. Unzip it, and put it in your GIMP script files folder. It will appear in the Filters-->SambrookJM menu...feel free to change that to wherever you would like. I've also attached a sample gif of what it looks like with 32 lines.
Getting rid of all of the commented code will connect each of the lines to the ones next to them to get a nice curved surface.