I like the idea of forwarding the real Jane one of the emails you received, preferably something important and/or personal, with the additional message, "I have been receiving emails meant for you for some time now. Please check that you are entering your address correctly." Or something like that. I think that would hit home for her the kind of thing you've been receiving, that she doesn't want out there.
You might want to put something in the subject that will catch her eye. I have my email set up to shunt all emails that are not from my safe list straight into Junk, and every couple of days I skim through that for the occasional real thing I need to rescue. So if this was you and me, your email would go to my junk mail folder, and I would probably think it was actual spam unless the subject intrigued me enough to open it.
If she seemed nice in her response, I might forward other emails to her--old ones that I'd kept, or the occasional new one to help her get things straightened out. That would be nice, above and beyond polite. Otherwise I would just keep deleting, maybe occasionally reply back to someone that they've got the wrong person.