To catch the Edges of the long bar, you’d need 2 AO Nodes, with one set to Inside, something like this:

But stick to the Pointiness if that gives you the result you want. (The problem with Pointiness is, that it depends on the Vertices, the more Vertices, the more accurate the Pointiness.)
I was just worried about the Bevel Modifier not working correctly. That would most likely mean that there is a Modeling issue.