It's a bit confusing because your model R I can't find info about anywhere but the model B does have Windows 7 support. So it's difficult for me to make a positive assumption about whether it's the router or not. I don't like telling anyone to purchase routers unless i'm pretty sure that is the problem. The R model isn't on that list as you can see, so we can only hope for the best.
And yes, beyond any shadow of a doubt your network problems mirror that of others with Windows 7 using incompatible hardware. This is a very very typical problem.