Given the option, he should have chopped it into pieces, burned the pieces into ashes, and flushed the ashes into the sewer. But this Lutheran stands with the young Catholics, who seem to know the faith much better than their neo-pagan elders.
As an alternative to the Tiber Toss, they could have got one of those chainsaw artists to carve the block of wood into a statue of Jesus and Mary, or crucifixes, or something. But the toss was ok, too.