After reading of your issues with your LS, I'm not sure whether the problem is the dealers service dept. inability to find the core problem, or it is possible you just bought the dreaded lemon.
I have a 2012 g3033h, that has never been back to the dealer shop since they day I bought it. The only thing that ever needed to be fixed was an o ring that leaked, which I did myself.
This is one of 2 tractors that are operated in my commercial vineyard by many different employees over the years, which increases the odds of some kind of product failure. Yet so far, nothing needed other than regular servicing, which I do myself.
I wouldn't blame you for going with a different brand next time, but if the financially, the deal favors LS, I am certain you won't see the same issues on the next model.