I’m glad to hear working with a team with Tiled is working out well for you! It was indeed an obvious choice, since using absolute paths would have caused so much trouble. 
Of course, even relative paths can end up pointing to the wrong location. In Tiled 0.15, one of the most important improvements I made was that any file reference can be fixed up when opening the map. Before that version, the map would fail to open and the only way to fix it was to open the map file in a text editor in order to correct the paths.
Btw, are the files also kept in a version control? I think Google Drive is a great tool for collaboration, but it’s probably not a good way to keep track of changes and backing up old states.