Here's a tip, gathered from my mad l33t google skillz (I actually own a book on google, you know).
http://www.stink.com/web/webtile/index.html
I don't know exactly how relevant this is, since seamless web tiles are a lot simpler than maps, but some techniques can probably be imitated.
If you use Photoshop or the GIMP, try drawing the troublesome province in the center of the screen, then offsetting it. The idea is that you're always drawing in the center of the image, but you change what the center is.
http://www.cadtutor.net/dd/photo/seamless/seamless.html
http://www.pixelpoke.com/Tutorial%20...0tutorial.html
I hope some of these links are useful. I can help you with just about any Photoshop, Gimp, MS Paint, or Paint.net question, but I haven't created any wraparound maps. I did think that seamless tile techniques may be useful for you, though.