I also love turquoises! I think there's also another frame that could be used to create a turquoise tiara. If they would acquire 5 large round turquoises ( no that expensive) that match his set and grab some small diamonds from the collection to create 5 clusters, then all that's needed is mounting them on the Pearl Button frame and voila!

As for the 'Emerald' tiara... They should finally remount the two oval clusters that were taken off and add two more smaller matching clusters and create a true emerald tiara. The current piece is neither here nor there....