Finding 1st-Degree Connections for Target Accounts Using Sales Navigator

I've gotten a request to find all contacts that have 1st-degree connections with someone at our company for a set list of ~4k target accounts so our sales team can name-drop the connection. The only way I can determine to do this with Sales Nav is running a separate search for each current employee (there's a feature that would work if everyone had Sales Nav licenses, but alas, 90