My vote would be for refactor. Two reasons. You've missed on big disadvantage from the rewrite option. You won't have a working system for some time. If you're refactoring you'll always have a working system.
We might not end up with the new ideal architecture, because refactoring works on the code level, not on architectural level.
I think you will get your ideal architecture, or at least you can get there with some tiny rewrites on top of a lot of refactoring. That's been my experience anyway. The architecture is, after all, embodied in the code. In general I've found incremental change to be a far more effective technique that a rewrite from scratch.
Take a look at Working Effectively with Legacy Code and the Strangler Application pattern for some ideas.