Paul,
Titebond should be the glue of choice - see if you can get as much in there as possible. Having seen someone glueing a back of an acoustic with Titebond (3mm wide join along a 50 odd cm length), then wanting to pull the two halves apart and ending up breaking everywhere apart from along the join, I can't see why it won't hold. Difficulty will be getting the glue in. In terms of the ridge, you could go with a gentle sand? Titebond should hold and you should be right. Should being the operative word. Given you're in Vic and all I'm hearing on the radio at the moment is about the fires in Vic as it's so hot, is there somewhere else you can store the body for a couple of days / weeks to stop it from cracking? Long term, once it's a guitar it'll be stored inside, so should be right - that's assuming it's being stored somewhere hot at the moment...
Hope that helps.