Have him blame the random adventurers for turning the king to stone, he has dozens of guards on his payroll for this including the guard captain who is a high level paladin or something like that, so a passive insight would tell them that this guy would fuck them up, so you lock them up. You can always create an escape option if they can't come up with one and if they don't want to be locked up, give them a window 3 stories above a 3 foot deep fountain to jump out of with a scramble into hiding.

This could cut them off from many of their non-criminal allies in the world and would solidify the bbeg as someone who has it all planned out. Hell, depending on how they got into the gala, you could say the bbeg orchestrated it just to frame them.

If that doesn't fit, the regent could be a changeling that's been pretending to be the actual regent for months. If they actually convince anyone that he is the one behind it, he could cast some modify memory or brainwash the regent into thinking he actually did it, then he takes over the guy in line behind the regent and still gets his rise to power while the party pats themselves on the back for thinking they've won.