Sucks that your beloved bike got stolen and am hoping that it comes back to you in one piece... I am still bitter over my first and last stolen bike as after a while they become more than just objects but a repository for many good memories.
If you go with green cork or cloth I'd consider using clear shellac to seal and protect it... it costs very little and will extend the life of the bar wrap by many factors and not have an unpleasant effect on the ride quality as the damping of the base material is retained.
Will look forward to seeing the finished bike and wonder if you've considered a tandem for touring instead of two singles ?