I think you can keep the edges pretty crisp and sharp when using this technique. It will provide results similar to what your seeing with your text / font work there.

Ignore the DPI number and just work exactly twice what you finally want to end up with. The DPI number depends more on what the final artwork is intended to do. If your planning to print it poster sized for viewing up close then you need a lot of DPI. As a guide only tho, 200-300 final is fine so find that pixel size and then double it when creating it then average your 2x2 and half it again for the final copy getting back to your 200 dpi or whatever you chose.

There is an option on most paint packages where you can average 2x2 pixels together so that when you scale half size its as though it was one pixel but correctly aliased.

But you have to like your own results and you have to enjoy the process of making the map. So if your happy with it then stick with what you like and enjoy the process. I only mentioned it because people would generally consider the jagged edges of lines a technical limitation of the raster process of paint apps, an unwanted aspect that the artist never intended.