The samples do go inside the alchemy cabinet, yes. Just not on display. I did not try that white box, I didn't think of it. Oh, a platform or something might work. I already came up with an alternative plan for mausoleum items, but these are still a good idea.
By the way, do items you clone using the Science skill count for mausoleum items? They're not on the list, I know, but I just wanted some clarification.