Recommend using neoprene contact adhesive with a small brush. There's a guy that sells amber color on ebay in small quantities, Herco brand, search 'neoprene contact adhesive'.
I usually divide the contact area into 1/6ths. Brush adhesive on the lid, then brush sections of the weather-strip and stick it.
One other tip on the repro stuff is to rough up the contact surface of the rubber with some 80 grit sandpaper to give it more bite. Also make sure any release agent is removed with a solvent.