I also garden entirely in raised beds (and some buckets).
I find weeding easier once I've amended the clay enough that I'm strong enough to pull roots OUT ... and their grip on the soil is weak enough that the root comes out instead of breaking off.
Fortunately, the walls of my beds can be leaned out and replaced easily. Once a weed has grown right up against a wall, or in the crack between two pavers, it is hard to pull or hoe.
A coarse bark mulch (or wood chip mulch) prevents most weeds and makes pulling really easy.
I haven 't used a dripline long enough to tell this from my own experience, but I've been told the INTENT of drip emitters is to water only one tiny spot at the surface. The water spreads around underground, but the surface is 99% dry. No blown-in weed seeds can spout on the surface.
