I'm not entirely clear on what you are after but I suspect you are getting into territory where you may need a GIS.
G.Projector only has 2 degree graticules. In a GIS, you should be able to track down shapefiles of finer graticules; NaturalEarth has a free 1 degree graticule shapefile for instance.I want to be able to have a very fine graticule down to single degrees at the very last (preferably minutes).
G.Projector can do this just fine.I cannot seem to import a pre-existing shape/continent as a black and white image and then specify the latitude and longitude limits of the map, the projection I want to use
I'm not entirely sure what you mean here. If you want to be able to apply a bunch of graphical glitz, and then reproject it and have it come out looking OK, that's not going to happen. The best you'll get is working with vector data in a GIS where you can set up your symbology (which doesn't include all the filters and whatnot available in a graphics editor) and then you can reprojected the vector data, and the GIS will symbolize the projected data.it's a destructive way of editing
This is the result of noodling around with your map in QuantumGIS
I've attached the shapefiles I made. It's pretty rough but it works. Learning to use a GIS is quite an undertaking though.