Shaded with edges view not working properly in Assembly

I am having trouble with a subassembly not displaying properly when inserted into a larger assembly using "Shaded with edges" mode. As shown in the attached file, "AssemblyGood.jpg", the file looks fine when viewed as its own assembly. However, when this same assembly is inserted into a larger assembly, it now displays as some weird buggy hybrid of "shaded with edges" and "wireframe". See the second attachment, "SubassemblyBad", for a screenshot of the same area - but now there are a ton of visible lines that shouldn't be there and it looks awful.

I am not sure if this is a directly related problem, but elsewhere in the same master assembly file, there are some features that have similar display issues, but they are all just parts, not subassemblies. This is shown in AssemblyPartsBad.jpg (this should just show three cylinders flush with a surface, instead there is some wireframe showing the cylinders penetrating the surface).

Any help or insight would be appreciated.

SolidworksAssemblies