I am thinking you just need to pull off and recirculate more volume than you are used to doing. As another mentioned, the false bottom has a lot more surface area and larger openings, so there will be more grain making it through. The braided set up has a much greater degree of filtering (smaller openings), and the grain will set around the smaller surface, creating increased filter effect. I personally do continuous recirc with a pump, and it really does take a few minutes of circulation before I notice that the grain bits are no longer present. A few minutes of pumping is easily a gallon or two, if not more, of volume that is recirculated. Then, its probably another 10 minutes before I notice a good degree of "clarity" in the wort being circulated from the filtering effect of the grain bed. When I start my recirculation, I start with slow flow, and gradually increase it until it is at a pretty good flow.
I recently switched to a Spike brewing kettle with their false bottom which covers the whole bottom of the kettle, and have had a huge increase in my mash efficiency.