Been there, done that.
When you talk to managers, you need to talk business. Throw every reason you think important into the trashcan. Then build your case from the ground up as a business case. Show that it saves the company money or increases productivity. Basically, make the case that your proposal == more $$$.
If management has ever complained about IT being slow or unproductive or their new iPad taking a week to set up - that's your door. Show them how productivity would increase with the expensive IT guys doing the IT work and lots-cheaper help desk guys doing the cheap work. Make sure to use the word "waste" a lot, because it's a red flag to managers - you they leave with the fear that they are wasting company resources unless they follow your proposal, but without you having said that directly, because they have to think they came up with that conclusion themselves.
And read up on the bikeshed problem - include some trivial, easily understood parameters in your proposal that management can discuss and decide upon.
And finally, understand that there may be reasons you don't know about that could lead to your proposal being rejected no matter how good it is. I once got a project rejected that everyone agreed was good because the company was about to merge with another one and nobody wanted to make a decision in that order of magnitude (a few million) because management had already begun the "there's one of us in each company but only one position in the merged one..." game.