I agree with all of the above, except the choice of glues.

If you ever take your guitar in to a luthier to have the nut replaced, they will not be expecting to deal with hide glue. The usual nut removal technique is to apply a gentle tap to one end of the nut to break the glue bond. This is based on the almost-universal choice of either PVA or cyanoacrylate glue to reatain the nut.

A [u]small[/u] drop of either Super Glue (cyanoacrilate) or white wood glue (PVA) will serve to hold the nut in place.

As you have already seen, the strings will hold the nut in place very securely without any additional glue. The glues I have listed will keep the nut in place even when all of the strings are removed, without making trouble for someone who wants to replace the nut.