Well, a few weeks passed, and I hadn't finished the book. I had absorbed numerous emperors, including a number of Constantines, a Constantius or two, Justinian and others. Lord Norwich certainly packs it in: all the conquests, defeats, religious arguments, plots, sieges, blindings, mutilations, mutinies, marriages of convenience - the lot. But I was only up to the death of Constantine IV in 668 (murdered by an attendant with the soap-dish while he was in the bath). Part of the problem was that I had to give up reading the book in bed before falling asleep, as it's hard to relax with the thoughts of the massacres of 80,000 troops or the self-inflicted drowning of 2000 attractive maidens or the killing of 30,000 civilians in the Hippodrome (ending the Nika revolt) reeling in your mind.
But then I found the library had a condensed version of the trilogy (A Short History of Byzantium). It's still got many of the gory details (such as Pope Martin being thrown into prison with murderers and common criminals and deposed emperor Romanus being paraded for 100 miles or so on a donkey "his eyes gouged out and his face and head alive with worms..."), but it compresses the events a little. I've recently passed the bit where the Eastern and Western churches finally split, when on 16 July 1054 Pope Leo IX's legation led by Cardinal Humbert purported to excommunicate Patriarch Cerularius, so there's at least there's some hope of getting through the remaining years until the conquest of Constantinople on 19 May 1453.
How many of the details I'll be able to recall when we get to Istanbul is a different matter!