Copy ListObject with non-visibles NULL

I'm trying to figure out a way to get a copy of a table where any
filtered or hidden cells in the source end up NULL in the copy.

Is there a simple way to do that?

My best guess so far is:

1) Copy the range to a temp sheet and make it a table
2) Copy the filter (if that can be done)
3) In the copy, invert the filter (if that can be done) or set a property on
all Visible cells and then select cells that don't have that property
4) Set selected cells to NULL

If anyone has an easier way or knows how to copy a table in a way that keeps
all hidden/filtered cells invisible in the copy, please let me know.

Thanks.