If you like Burton you'll probably like Ghibli, it's not really morbid but it's otherworldly. But it sounds like you like action/triller stuff quite a bit too. Death Note might be good. It's about this high-stakes battle of wills between two geniuses, but guns do come out in the second half, and it's got a very dark atmosphere. If you just want straight action though I would recommend Black Lagoon. Everything is just so completely outrageous in the best way possible. It's almost a parody, but it still manages to be serious when it needs to be.