I have a 2011 LTZ with 3.6L as well. I've been using AmsOil Signature Series for the last 38K miles. I know that because that is when my engine was replaced after it threw a rod. I'm not convinced it was the oil I had used, which had been a number of different brands of synthetic blend. Royal Purple is what was in it when it died, but I'm sure RP was not the cause.
SS is the best AmsOil makes and may be overkill, but a number of unaffiliated tests have confirmed that it's good stuff. Look up YouTube's "Project Farm" channel and check out his comparisons.
The biggest things you have to worry about, as far as I've heard, are the timing chain tensioners. They're plastic strips stuck on metal backing plates. There are 3 chains and 7 tensioners! As it has been related to me, when the oil additives become too weak to do their jobs, it's possible that the plastic will wear more quickly.
I also added a remote oil filter so I don't have to deal with removing that dinky little thing and drip all over everything while trying not to burn my hand on the exhaust. It now uses a full-size filter mounted 100% vertically behind the right headlight. With more than twice (or 3x or 4x ??) the filter media surface it should be able to move more slowly through the filter, allowing it to filter out even more stuff.
I made a thread about it in the Gen7 section if you feel like moseying over there.
I plan to be changing my oil this Sunday. It's currently using a Mobil 1 filter and it's going to change to an AmsOil eA filter. It will have about 5K miles on the oil since the last change in September.
There's also a thread on here by @!Tommy
that asks members to share what they use and how they feel.
Don't forget to drain and fill your tranny. It's really easy. I've done mine 2x and this Sunday will be the 3rd. (Yep, you guessed it: using AmsOil tranny fluid as well!
I have 2 bottles from Blackstone Labs so I can send in samples of the engine oil and trans fluid. I've never done it but I'm truly curious about their condition and there's no better way I've heard of to get that kind of info than an oil analysis. $28 each. I hope it comes back with good news!