I ignore the volume under the false bottom when calculating mash thickness, then just add it to make up for it. For example, if there's a gallon under the false bottom and you're mashing 20 lbs of grain at 1.2 qts/lb, that's 24 qts of water, or 6 gallons, plus 1 gallon from under the false bottom and so I use 7 gallons of water in the mash tun.
Not sure if it's the right thing to do exactly, but it works for me.