1997 [?] – Lord of the Rings Three Volumes with Hobbit- Michael Herring Covers – Colored Covers; Web Address, Solid Price Box State – Mass Market Paperback – Ballantine

These have a web address advertised on the back (www.randomhouse.com/BB).  The earliest extant copy of this website on the Wayback Machine at archive.org is 1997.  So at a minimum they were being printed by 1997.  It would appear that The Hobbit, The Fellowship of the Ring and the Two Towers always have black boxed spine prices in this state while The Return of the King always has a white spine price box.  It is common (almost ubiquitous?) to see mixed white and black spine price boxes in the same boxed set.