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There's an allen set screw up in that hole you need to fish around until you find it. If my memory is accurate it should be a 1/8" or 9 /32" allen wrench.
The allen wrench is 3/32" according to the American Standard site.
I saw what you said. I'm telling you there is a set screw up inside that hole under the lever. I've installed dozens of these faucets and removed the handles on more. The screw is there but you have to fish around with your allen wrench to find it.
Of course you have to pop/pry the plug off to get to it
Have you tried an allen wrench? Here's the install instructions for your valve trim. As you can see they show an allen screw.http://www.americanstandard-us.com/assets/documents/amstd/install/Install_607.pdf