First off, can't open the attachment, you might try saving as a pdf or something.
The code is set up to design vessels, not so much to evaluate them, so if you apply code provisions and it turns out the item in question is actually twice as strong as it needs to be, that's okay per code, but not much help in evaluation.
With that in mind, yes, taking the wall section at the thinnest point and applying the formulas is about all you can do for simple solutions.
If the application is appropriate, using finite element methods (with a very knowledgeable user!) would get you a lot closer, as would testing.
Also, there is some data available for evaluating local thin spots in heads in ASME, and perhaps similar info for evaluating corroded areas in existing vessels that might be of use if the geometry was close.