It probably has something to do with Anders blowing up the Chantry and everyone's tempars running high. The first thing he says is that the Circle was not responsible and then he pleads to the champion to not let her do it. He has always operated under the opinion that Meredith was simply looking for a reason to annul the circle, which she was. Did you see that scene? Meredith was not hearing anything. She was dead set determined to wipe out the circle from day one of Act III if her sending the annulment to Val Royeaux is any indication, offering anything in that particular moment was probably the furthest thing from his mind. He simply wanted to survive.
In their encounter in the gallows it seemed that Meredith had regained her composure and he was trying to leverage in that fashion.
Or of course you can believe that he was hiding evidence.
This argument relies on observational skills which, of course, greatly differ between individuals unless it is just that obvious. I don't see any difference between the mental state of Meredith in those two events.
It is possible that it slipped Orsino's mind, I suposse. But it stands on very shaky ground.
Probably, and I'll be blunt and meta here, because the writers didn't want to distract from their intent of the emotionally charged catalyst on an irrational actor.
I doubt 'he wants time to hide his dirty deeds' was part of their writing thoughts at the time. Besides which, if Orisino was competent he would have long since already hidden the incriminating evidence, rather than leave it out in the open.
Probably not but, ingame, his actions raise some suspicions.
Your argument that Orsino would have already hidden it is compelling but remember that Hawke fights a great number of blood mages in the Templar ending. Perhaps Orsino was not willing to risk any of his apprentices having chosen specifically that night to be less thorough in concealing evidence of their lessons than one should have been.