I have the same cooler and that false bottom looks like the one I got from AHS (12") except that mine has a stainless steel right angle barb instead of brass (3/8" barb on top, but 1/2" on the bottom). In order to minimize the dead space, I cut a 1/2" stainless steel coupler in half (not exactly, maybe 60/40?) and used the shorter piece to replace the nut underneath the false bottom. This allows me to siphon out all but the bottom 1/8" or so.
I connect from the barb on the FB to a barb fitting on the ball valve with a piece of 3/8" silicone tubing with s.s. hose clamps.
I always throw a few ounces of rice hulls into the mash, more if I have something like flaked barley - this helps prevent stuck sparges and I've heard that it helps even out the mash temperature (according to Gordon Strong in "Brewing Better Beer").
One more recommendation - I've heard a lot of people complain about the lining on the inside of the cooler warping due to the heat. I suspect it may be more due to sudden temperature changes. I heat my cooler up gradually and so far have had no signs of warping. I have a kettle that I heat the water in - the output of the kettle goes to my March pump which pumps it to the cooler - the cooler is sitting higher than the hot water kettle. As I heat the water, I pump the kettle contents to the cooler, then turn off the pump and let the water drain back through the pump to the kettle (takes 4 or 5 minutes to drain) - when the kettle is full again, I pump it back to the cooler. The water is about 20º F hotter each time. It's a little bit of trouble to have to watch the pump, but worth it if it prevents damage to my cooler.
