The writer was James Goldman, not John, but otherwise I agree with every bit of your review. The Lion In Winter was one of the last gasps of Hollywood's old guard - by 1968 the studio system was basically dead - and while 2001 and Rosemary's Baby were robbed of Best Picture nods, there's no question The Lion In Winter was by far the best of the five films nominated for Best Picture. The fact that Oliver! took the prize is in hindsight one of the worst decisions the Oscars never made and this is one of the two biggest robberies of Peter O'Toole's career. (O'Toole had played Henry II before in Becket; he is the only actor in history nominated twice for playing the same role in films that are not sequels.)
I watched this film multiple times as a child and even at thirteen and fourteen its power never ceases to amaze me. It rarely gets ranked among the best movies ever made, possibly because few Broadway adaptations ever get that consideration. I often wonder why Shakespeare, who wrote so many plays about the British Monarchy, never did one about this struggle. But honestly, I don't even think the Bard could do as brilliant a job as James Goldman does in The lION IN Winter and that is a compliment to the masterwork he created.