Gotcha, I know where you're coming from, I'm 22 and not the tallest myself. Do you handload? If you just want to start out to 600 I would just go for an AR-15 with either a .223 Wylde, 6.5 Grendel, or 6 Hagar chamber (or some hi-pro wildcat if you handload). Large frame AR's are notoriously less forgiving than the 15's as semi's aren't the easiest to learn on. Have you tried measuring your length of pull? I had the same issue with my first rifle, a 700P, so I got a Mcree chassis, and the LOP is adjustable down to something around 10.5-11" which is comparable to an AR-15 with the stock collapsed to the 2nd or 3rd position, I'd have to double check. I would strongly recommend a bolt gun to start, as I'm getting into ARs now, and while I can shoot my bolts without issue, my semis are always right there to take advantage of any mistake on my part. The best rifle I own is my .22LR 40XB, and the one I have the most fun with because every time I start screwing something up I go back to that rifle, square it away within a few rounds and then I'm back to shooting my other rifles.
I'm not trying to discourage you from what you asked for, but the patterns have been made, and if you want to learn to shoot LR, it will be easier to start with mastering, and VERIFYING, the fundamentals on an accurate 22, moving up to a bolt gun to begin to learn wind and get DOPE, then move on to gas guns. Each time you're going to be adjusting to what's new with each system, and each will present new issues. Reducing the amount of variables will make learning easier as you won't have to figure out what your problem. Seldom are issues straight-forward or simple, most are compounded and indeterminate without someone more skilled there to show you what your exact problem is. I spent many hours trying to pin down issues with my .308 bolt gun and watched the online training over and over only to realize when I got my 22 was that I wasn't relaxed and had remaining muscle tension that was affecting my accuracy. Way easier to learn when you know what you're doing right.
Still, if you're going to get a .308 AR, go GAP.