Actually, this is not as resolved as I expected. I went back to my original situation and was reminded of the specifics of what led me to this dilemma.
While most of the custom attribute properties do seem to be accessible, there are some problems. Namely, the one property I actually needed in the process was a Material parameter. The CA (Custom Attribute) is storing a MultiMaterial for model skins. In this case, the attribute is named #wwmtSkinMaterial.
When I open the original scene, the Node with the CA has a MultiMaterial stored in the #wwmtSkinMaterial param. So if I select it and then hit $.wwmtSkinMaterial I get the material. But when the node is used as an XRef Object in another scene, the XREF always returns undefined for #wwmtSkinMaterial -- even though it can see the values of the other parameters.
This is what let me to believe initally that XRefObject.GetSrcItem() did not have access to the CA params... because the one parameter I needed and was trying to access is always undefined.
So the next question is how do you bring in an XRef Object via MAXScript and ensure that you also bring in all the parameters? Is there a specific command in the xrefs.addNewXRefObject() method to ensure this? I experimented with various values in the modifiers/manipulators.dupMtlNameActions and none seemed to make the material property of the CA accessible.
I can think of ways to accomplish by creating a new node in the scene that has that material stored on the object itself and XRef that node... but it would take rewriting many tools and changing who knows how many existing asset files... which is certainly not what I'd like. I'd like to figure out a solution with the tools at hand.