Since there is a current limitation of not having one person able to be associated to more than one organization, is it possible to implement something like the related organization field so that we can at least associate people to orgs in more flexible ways? 

I created a custom field to do this at the org level, but it does not associate both ways. having a related people field implemented like related orgs would at least provide that ability.

And, I'm still hoping that you revisit the decision not to allow a person on more than one org.