1. Install the add-on.
2. Panic that it has deleted all "not open now" websites' cookies.
3. Choose the option to "Suspend Operation" via the add-on icon.
4. Repeatedly "Undelete" all cookies until it's all done.
5. Keep the add-on suspended.
6. Now, for the next few days, I will browse like normal, but will remember to "whitelist" the websites I like to stay logged-in (Hacker News, Webmail, etc.) by clicking on the add-on icon. Remember, it is still "Suspended".
7. After a few days of usage (and when I've re-visited enough number of my regular websites), I will "Resume Operation" on the add-on, where it can start destroying the rest of the cookies like anything.
I think the "Training Period" above in point 6 should have been by default. Somehow.