Hahaha ohh how will Atlas deal with this gambit? Well. In truth its probably best he remains quiet. He'd probably just confess to committing the crime himself, flippantly admit that the next part of his plan was to be exactly where he's standing so that he could assassinate these weak ass politicians. xD Although, they'd implicate Vincent, so Atlas wouldn't do that.
I got a few questions. Did they disarm the seven? Also, is there any sort of trial by combat feature that the players could use as a last ditch effort? 
What would also be some of the rumors spread about these politicians that might contain a nugget of truth? 
There must be something we can use to acquit us of immediately being condemned to death. A sort of political or occult loophole that we can exploit.