i used to have the same set up but now i use a converted keg for my MT. at any rate the following set up will be the same in the 10 gallon gott or keg.
go to a grainger store in your area or buy online or go to a cleaning supplies store. get a 3m white polishing pad. yep i said polishing pad. if i remember the 10 gallon gott uses a 15 inch but measure to be sure.
assemble thusly:
take your mash pad - leave the center ring in it. cut a small hole in the center so that your tube from the false bottom will fit up through. false bottom goes in the cooler - mash pad goes on top the false bottom with the tube threaded through the hole - connect tube to ball valve as normal...and your stuck sparge worries should be over. baring of course you drain the mash tun slowly as you sparge...sparging should take an hour or so - ie follow procedures normally.
the center hole is out on this pic to better show assembly