Idea 2 seems better to me, though I'd probably keep it solid in the area between the pickup and the neck pocket. There will be the upward pull on the neck joint from the strings, as well as an inwards compression force, so I'd suggest making that area as strong as possible.

If the strap button is going on the end of the top horn, just make sure the wood is thick enough to take the screw without it poking through on the inside. I use Schaller straplocks and always use the longer screws they come with for a bit more security.