Tableau only can go the zip as the lowest level when geocoding. You need another service to generate lat and longs and use these instead of the Tableau generated ones. I use this web service:
Run your addresses through this and then save the results with a Latitude and Longitude column added.
Another option might just be to highlight the ZIPs that have multiple projects for the same ZIP visually on the map (using colour, shape or size) and then have a filter action to take you to a detail sheet showing the projects for that ZIP.
Superstore sales example attached (orange means multiple customers in same ZIP, blue means only one). Hover over a ZIP and then follow the menu link in the popup to the other sheet. Would that sort of approach help in your case?