Nice question for us. This is fun to chew on. I'm in a similar situation except that the big application that needs re-writing is my own! The other folks have given most of the important advice that needs to be given, I'd just add two things:

1) It's a mistake to think you can be rigorous and implement a system top down, or bottom up. My experience is that you've got to go both directions at the same time to get good code.

2) Don't try migrate the current code into the new solution. No matter how good you are, you're bound to break it at least once as you go along, and I'll bet you don't end up with anything nearly as nice when your done. Also, if you develop on a test system, you'll find that some of the "new" features that you add into the new system are completely independant of the current code base, so you can "paste" them in to the live site and get that functionality anyway.

-I went outside... and then I came back in!!!!