I'm sorry but there's nothing like the product you mentioned about coming anytime soon. There is simply very little demand for such a product, especially with such a big screen
Id take 13 any day. Graphics boost isn't that significant but the 13 is simply a nicer sized computer. I think battery life is probably the same or in favor of the 13in as well. They is very little reason not to pick it if they cost the same.
This ones well under your budget but it has a decent CPU and a midrange GPU. I don't think you'd gain much gaming performance spending any more money to be honest with you. http://m.newegg.com/Product/index?itemNumber=N82E16834312434
You can check temps for your components, they might be holding your performance back. The parts may be downclocking because they are thermally constrained. The only other thing I can suggest is to send your machine off for repairs if it is under warranty. Did the laptop always perform like this?