Sharp writes that the Central Triple is a natural, and powerful, extension of the Anschluss, so you're ignoring a decades-old solution to the Italy problem - let him in on it! Italy and Austria are weak early, so having them fight each other is senseless. Germany might propose to Italy that he attack Austria, if Germany has a sensible alternative plan to the Anschluss, but he'll take advantage of the distraction to sort out England and France, not to send armies charging against Austria.
Now, another issue is that, if things work out and Austria goes down, the gains will accrue to Italy's true ally, Russia. I/R is extremely powerful, and finally offers the underpowered Italy a real chance (a draw or a strong second). Remember that the Anschluss profits Austria in the early game, but GERMANY in the middlegame, because it provide a powerful buffer against Russia, while making sure any Italian aggression is met swiftly and decisively.
The extension of the Anschluss to the Central Triple facilitates a game-breaking stab by two of the allies on the third at some point. In my experience, it's been easier for Germany and Austria to stab Italy, but I think that's an artifact of poor play across the site - I think it makes more sense for Italy and Germany to attack Austria, but not early, as you propose. France and England should be sorted out before a stab, and Russia should be significantly weakened as well.