The splints in the slots are useful when I am saving an original ivory nut, or when I just need to raise one or two strings.
When shimming the bottom, I glue the wood shim to the bottom of the nut with CA, but I normally run the grain the length of the nut, not parallel with the grain in the neck. If it is stained on the ends to match the neck finish, it it not that noticeable. I don't like to shim if it would be thicker than the depth of the slot.
Although I have no reservations about shimming a nut with paper, I rarely find that it is thick enough.