They are very happy to show you the contracts- but as you predicted, you'd need Law to make something of them.
The Courts do tend to expedite things when the Jedi request them... but only relatively. They are indeed dead slow; the warrants you got for the pirates at the start of the episode took days.
Jedi can act unilaterally if they believe that the public is at risk- but you had better be damn certain about it. Or have a Senatorial ally to back you in the investigation that follows.