I would follow Mort's advice about putting something over the diptube. I've used a stainless braid and it's very effective at drawing clear beer and leaving sludge behind.
I've got some stainless tea infusers that I use, but for the price if I did it again I would probably buy the gizmo that Hoosier uses. I don't find that too much sludge gets through the mesh of the tea infusers, but if you're concerned the stainless braid does a great job. It's better to plan ahead and install it first, but I've also installed it in full-ish kegs.