George has already confirmed in several interviews that Joffrey sent the Catspaw. Within the books, both Tyrion and Jaime reach the same conclusion independently. The case is closed. And yes, it's not a particularly well-constructed mystery. The resolution is forced and requires leaps of faith from the reader. And the red herrings from the first book are even worse (Littlefinger absurdly claiming that Tyrion had won the dagger betting against brother was a stupid and transparent lie).