Its clear the writers don't know what to do with Littlefinger anymore
Whatever he's playing at (and I didn't clearly see what it said on the scroll Arya found) it seems really unwise at this point. With the dragons and the WW coming front and center, political machinations have become irrelevant and pointless. Knowing his character, you'd think he'd be smart enough to realize that and just let things play out.
He's overplaying his hand. This won't end well for him. I think the writers are just looking for a quick way to write him out.