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Thank you for moving from the github issues over here, and for your very detailed question. It helps out everyone who has similar issues.

The only currently known issue with regards to masses and inertia properties is that the exporter does not support overridden properties, and it would be difficult to support that with the current workflow of the tool. However, it would be an unknown bug if the combined mass properties of a selected group of components (with no overridden properties) in SolidWorks does not match the same list of components in a link once exported.

When comparing the two though, make sure that you set the reference coordinate system in the mass properties dialog, otherwise the properties will be in reference to the global origin in SolidWorks. The inertia properties in the exporter dialog are always in reference to the link's inertia origin, which is the center of mass and aligned with the link's joint origin. The inertia matrix in the example you show does seem to match the inertia matrix in the mass properties dialog for the one taken about the center of mass and aligned with the output coordinate system.

You are correct that you will need to include both the hidden components and the skin components as the components in your link in order for the mass properties to match the solidworks components. The advice I give everyone when exporting from SolidWorks is to put all the parts and assemblies for each link into a single SW subassembly, which would include skin parts. If a link is just a single part, then you can leave it as a part. Also make sure that you set the mates so that the link assembly has the representational degree of freedom of the link in your robot. If you include many components in the selection list for a link, it's harder for the exporter to know what you want. It may also be possible that there are still bugs when there are multiple components in the selection list.

Please let me know if that helps to answer your question. That's an awesome looking robot!