There's two ways to go about this one. The more ultimately satisfying one would be to post your attempt, tell us where you think you went wrong or what steps you're having trouble with, and you'll get a lot of helpful tips and advice, and learn more than you ever though possible. You'll likely end up with something you're very proud of - and have the satisfaction of knowing it's all yours.
That having been said, I understand the level of frustration you describe, can't be easy knowing you're under time constraints while learning something new, heh. I've started playing around with the map a bit myself, testing out a few things, and it's actually coming along very quickly. I just needed a break from the other projects on the go, heh. And I'm learning a few things along the way while I mix and match styles, which is another bonus
You didn't really say what kind of style you were after, so I jsut went with my first impluse. An antique/hand drawn style would actually be quite a bit easier, it's got a decent base to start with.
Anyway, here's what I have so far.. (but I still highly recommend picking one tutorial that catches your fancy, and posting your progress)
Oh, I should probably ask about that river, it would be unusual for a river to choose to go through a mountain range like this one shows