You have to use a mortise and tenon because your neck is angled back to match the carve of the top. You might be interested in comparing the neck joint of a Les Paul (Gibson in general) to that of a Paul Reed Smith. The Gibson body has a block sticking up to mate with the neck which has a matching heel and the tenon that you can't see. The PRS body lines flow continuously without the block area for the mortise. The neck mates with the body along its curves; the mortise is just a hole in the top side. The PRS style is much easier to manufacture because you don't have to accurately align the block with the heel of the neck. Gibson customer expect the traditional design from the handmade era. You can angle the tenon or slant the mortise its your choice. Think about how you'll hold your neck to machine it and how you'll machine the various angles before you choose.
Your approach to machining the body sounds workable to me. I've got LP's if you need a measurement or something.