Alright, I am with you half half. I am going to try and set it up the way you suggest and give you feedback.
Instead of setting up the additional mailboxes on the workstations, we set up a single exchange mailbox (e.g.ReportRequests). We then grant access to that mailbox to the AD group (DataWarehouseTeam) that needs access. Then, in Outlook, each member of the group adds the ReportRequest mailbox in the Exchange Account properties. This gives them access to both their personal set of exchange folders as well as the ReportRequests mailbox. You are able to select the account you use on outbound and all inbound are seen by the entire group.