Devken
Have you tried to use a pre emergent like Preen on the garden. That will cut down on the self sown seeds and let the perennials thrive.

How is your project going? I see that you posted this back in February, but nothing since then. I'd love to see a progress report. Or are you out there pulling weeds until you're blue in the face? Cheryl

Pull as many as you can of the plants you don't want, and apply 3 or 4 inches of a good organic mulch to keep weed seeds from sprouting as readily. Those that do germinate will be easier to pull because the mulch is soft and keeps the soil more moist, and over time the mulch will break down and improve the soil even further.