I used the false bottom with the dip tube on my last brew. I didn't get a stuck sparge, but I did get some particulate matter in my run off. I used just the bazooka tube when I boiled, and it strained the particles out well (think the whole hops helped clear it too).
I am very interested to find out how your mash turns out with just the bazooka screen. I have considered switching to a copper manifold and ditching the false bottom.. But if you get good efficiency with just the bazooka, I don't see why that wouldn't be the way to go. Are you fly sparging or batch sparging? I've heard that when fly sparging with a bazooka tube that channeling might be an issue, but I think as long as you get good distribution of sparge water over the grain bed it should just work fine.