There is an easier way to fix it: Incentivize safety. Get rid of the TSA all-together, and charge the departing airport for the damages caused by any attempted or successful attack. The airport will have to balance the risk of an attack leaving from their location with the risk of losing all their money from people not flying. It's the same calculation they use (more or less) when they buy their insurance, so it should be a no-brainer.
On top of that, actually punish people for willful violations of basic constitutional rights to keep whoever the airports hire from getting too big for their breeches (unlike the TSA...), and the problem -- if it actually exist -- should resolve itself.