He's gotten rave reviews for his performance in Richard Linklater's Me and Orson Welles, which to my knowledge still doesn't have a distributor.
And I refuse to buy some of those flicks as artsy departures (I DID mention Before Night Falls, btw). Tim Burton's post-Batman film, even if weird, doesn't make it a huge box-office gamble. Burton's whole appeal is the weirdness-- that's why his film were doing well, and why they do now. Also, Donnie Brasco, fresh after Four Weddings and a Funeral for Mike Newell, and starring Al Pacino, isn't a box-office gamble either. Finding Neverland was on the heels of a Oscar nod for him, and it's a biopic tailor-made for more Oscars-- I don't count Oscar bait as artistic risk.
Like I said, I like Depp. I just don't think he's ever been a model of artistic integrity at all. He's like every other Hollywood actor who likes to do an indie flick in between sure thing Hollywood material. That's not artistic integrity, it's just wanting to be a better actor.