Signalling is a lot like standing up at a baseball game. It gives you a great view, at the cost of having your legs get tired. Once everyone else starts doing it, your view is no better than before, and everyone is a little more tired than before. But no one can sit down, because they don't get to see the game.
A tax on signalling might reduce the benefits and thereby reduce the amount of resources wasted. Additionally, the people who don't engage in signalling would enjoy reduced taxes.
To begin, I'd propose an education tax, since education seems to be our nation's most expensive form of signalling. You want an education? Fine, but be prepared to pay an extra $5-10k/college year to compensate the people who don't get a job as a result of the degree inflation you cause.
(Obviously, ending subsidies for higher education would also be a good start.)