HolyDiver, 2200 rounds is a weekend shoot. Your barrel isn't even close to being shot out. How long it will go, in terms of number of rounds, depends a lot on your shooting habits too. If you like doing mag dumps, this will likely reduce the life of the barrel. If you're shooting consists of aimed, deliberate shooting, it will last a lot longer.
Like I said before, changing barrels just to get chrome lining isn't going to be much of an upgrade. Personally, I think it'll be a waste of money at this point. I've run chrome lined and non chrome lined and haven't found one to be any sort of advantage over the other (except that chrome cleans easier). I very rarely clean my plinking ARs. Yes, chrome lined chambers are slicker, but if having a chrome lined chamber is going to make the difference between your rifle continuing to run or not, then there's something else wrong with your rifle. I've never seen a properly running AR stop running because it was dirty. An AR will run as long as it is properly lubed.
That stuff about steel cased ammo being "sticky" is a bunch of BS. They aren't any more sticky than brass cased ammo. The main difference is that steel cases don't expand and contract at the same rate that brass cases do. There are generally two problems associated with running steel cased ammo. The first is that it is under powered and causes short stroking. The second is that the ammo isn't under powered, but the rifle is over gassed. In this case, the extraction process starts before the case has contracted and the problem manifests itself as a stuck case. The problem isn't that the chamber is or isn't chrome lined. The problem is that the rifle is over gassed. With this second situation, I'd argue that a mid length gas system would reduce the likelihood of stuck cases, due to the lower operating pressure (assuming that you aren't using underpowered ammunition).
In short, if you really want an upgrade, go with a midlength. Changing things just to get chromelining is a waste of money and will get you no tangible benefit.