How do I use embedded data from multiple contact lists without updating the survey each time?

Hello all,
My company sells some of its products through distributors. These distributors also have help desks that serve as front line support for our products to their customers. Each month, the distributors send me a list of their support cases, and I have to send out a CSAT survey to the customers on that list.
I want to set up one survey that I can use for each of the distributors. And I want to use embedded data (distributor name, case number, case close date, etc.) in the survey for analysis. If I get the embedded data from the contact list that I use as a send list, then I'll have to update the survey for each send (per these instructions).
Right now, the only thing I can think of to get around this (and still use embedded data from the contact list) is to create a master list, which is the union of all the send lists. Then the survey will use the master list for the embedded data, and I update the master list before each survey distribution.
But there's a problem, if a customer opens multiple cases with a distributor, then I will overwrite the previous embedded data with the new data, which I definitely don't want.
Is there another way to approach this problem? Do I need to set the embedded data using values in the URL?