A few more things, too many to warrant an edit of my prior thread. My router problems were caused by a broken router, so I purchased a new one and it works fine. But, and I imagine someone might have a similar problem, the new router worked very poorly with Forza. They use a different sort of protocol than every other game, so it's possible that though every other game works fine, Forza won't. Fortunately updating the router's firmware seemed to solve the problem.

I'll also finally be going through and adding everyone's gamertag to my friend's list in the next few days.