Without seeing the data set, this is difficult to answer. However, based on what you describe, the most common way I would have attempted to handle this kind of situation prior to LoD calcs in v9 was to use the self-blend technique. In this, you duplicate the data source (which does not duplicate the data, just the connection to it), and adjust the links between the data sources so, for example, one is filtered for the origin facilities, and the other by zip code. I'm not 100% sure that is what you are looking for, but it is a general direction.
If you can attach a packaged workbook (.twbx), we have a much better probability of being able to help better. If you have confidential data, please see Anonymize your Tableau Package Data for Sharing |Tableau Support Community.
May I ask one more question: why are you still on v8.2? I think that is now 17 months behind.