Forget the truth potion. Why din't someone take the elementary step of seeing what spells Sirius Black's wand had cast? At the very least, they would want to know what else he had been up to.
Since they had waived the rule about the Unforgivable Curses, they could try them, too. Command, "Tell the truth." All right, you would need some way to verify that they weren't shaking it off, but it would be better than they had.
Or the Pensieve and the liquid memories. True, we saw how Slughorn could meddle, but rather badly. Just a little improvement in detection, and you could exonerate yourself by showing what really happened.
Ah, the possibilities!