For that type of music the AM seems like a fit to me. The neck can do the ambient sounds very well and the bridge can riff the shitee outa you. So if you dig the bridges desert dry über tight center mid focused sound I say you are at the right adress. (I for one love it in my super heavy LP style axe). Plus it should have no problem with the tuning.
About covered or not...you have seen the video and know there is a difference. If you do not immediatly say one is a lot better I suggest you go by looks. The difference is not that big and if you get covered ones and find the high end ever so slightly too tame you can pick harder, use different pics (or pic materials), use different strings, somewhere in your signal chain add a tadd of treble,...
Thing is both covered and uncovered would look great in that cort^^ Personally I though I think I would really dig something like a chrome or nickel cover most.