As you've mentioned in your post, the Stud sems to have a problems with the construction planes.
Actually it would appear to me that F360 has a problem with exporting parts that include construction planes as part of their design, as well as with importing parts with construction planes!
I had come across this before, but forgot about it. When first transfering this Lamp desing into F360 I dind not exactly understand how to create a reusable components and basically had to toss my first assembly. Then, as backup measure I designe all the single parts in spearate file so I could re-insert them if I screwed something else up, or in case another assembly file became not recoverable (The fact that a referenced sketch cannnot be moved into the (only) component that references it is hard to believe and a rather blatant oversight!!! ).
Anyway, the first thing I did in the single compoent file was to create a componet and then the sketch for the base extrusion, then the body for the base extrusion etc.
However, if that file is inserted it will turn into an asembly with exactly one component in it. That was not what I had wanted, so I opened each single file and exported the component to eleiminate the unneeded level. These exported compenents had probelms with the construction planes and I had to re-select them in each file. That was not immediately apparent when opening each single file as there were no yellow highlights in the timeline.
However, the Stud now is also in that project as a single component file. A Compute All in that file does not return any errors. I did not touch the Stud design after I inserted it into this Lamp file, so F360 does "someting" with the construction planes on import or during the design provces that's not qite kosher!
Long storty short: Construction Planes need to be looked at!