The stock batteries suck balls. My '10 LGT never instilled much confidence in me when turning the key.
I'm not sure if the 3.6r uses a bigger battery, because that thing fires right up with no trouble at all, whereas I'd cross my fingers much of the time turning the key in my '10 LGT. Of course my LGT sat on the lot for a year before I bought it, so who knows, maybe the battery it came with just wasn't stored well.
I say just get a better battery, you're going to have to replace it in a couple years anyway tops, might as well replace it before you get stuck somewhere.
FWIW, I have carried a jumper battery pack in my trunk for years. $70 for insurance my car will always start is a small price to pay.