Ah well, that's just pretty poor isn't it? Adobe need to get on top of that don't they? I mean, how many developers create loads of small applications that can be developed once and then used on many sites!
I know I do, and I have struggled with this often, but I am now using a lot of sessions and it's becoming laborious to have to figure how to overcome issues in sites that don't work because sessions are missing.
Perhaps there could be an addition to the security assist extension to be able to import sessions from other sites, or even run a script to recognise sessions in pages are copied in to the site to populate the bindings panel.