Should America be in the game as they are just a colony that broke off from England?
I think the American civ could be broadened into an Anglo Saxon/English Commonwealth/American civ. Then the English civ could represent a Norman/Plantagenet/Tudor/Hanover/Windsor civ.
Mostly because many of the claims towards American Independence were predicated on Monarchial skepticism which traced itself back to the previous English civil war in which England briefly became a Republic under Cromwell, even further back with the Magna Carta (which unsurprisingly inspired the parliamentarian roundheads against Charles II in the first place). Also Thomas Paine in his pamphlets frequently questioned the legitimacy of King George III since his blood line could be traced back to William the Conqueror who was a Norman Conqueror and not a native Anglo Saxon king such as Alfred the Great.
So technically you could keep the American civ as a sort of anti-Norman lineage based English civ. The rest of the Anglosphere can be left out since they all currently accept the current bloodline (that is King Charles III) as their legitimate head of state. The United States, the English Commonwealth, and the original Anglo Saxon kingdoms being the only past and present parts of the Anglosphere which reject this premise. You'd just need to add Cromwell as a leader of America as well as transfer Aelfred over and replace him with William the Conqueror for England.
The same with Brazil as they were a colony that broke off from Portugal.
I guess there was more racial integration/diversity (though there was still chattel slavery of Africans) with Brazil whereby the Tupi are incorporated as part of the Brazilian civ (I mean there is conflict between natives and city dwellers in Brazil but it's more like the city dwellers are at least mestizo, that is half-white half-native). Not like the good old racist United States which sort of exterminated it's natives rather than adequately attempt to assimilate them (that is intermarriage to form a significant mestizo population like all the Latin American cultures) or respect them as equal sovereign entities.
I do not think the Byzantines should be a civ under your criteria. The term Byzantine is an anachronism. The "Byzantines" called themselves Romans and the Byzantine Empire was just the surviving eastern half of the Roman Empire. I would add some of the Byzantine leaders to the Romans and get rid of the Italian rulers for the Romans. Maybe add the hippodrome to the Romans.
I'd remove the Byzantines and add all their leaders as Greek leaders since there is not a lot of Greek leaders and modern day Greece was created by attempts to reestablish the eastern empire as many Greeks at the beginning of the 20th century still considered themselves to be Eastern Romans. Romans looked up to Greek culture and vice versa, at some point all the eastern emperors became Greek Speakers.
This would then free up a free civilization slot which I would turn into an Etruscan/Lombard/Italian civ, put the Italian leaders from the Roman civ into that, plus add an Etruscan leader or two, maybe a Lombard. Finally take the Roman civ and add a Pope Leader to represent the Papal States/Vatican and Romulus to represent the Roman Kingdom.
There should be some more Makedonian representation for Hellas (Greece). I would replace the trireme or hoplite with a phalanx or phalangite. Or maybe a separate Makedonian civ.
I'd just leave Macedonia as part of Greece. Even though Alexander wasn't seen by the Greeks contemporaneously as a "True Greek" but a "Macedonian Barbarian" later on he become considered a Greek based on his glorious achievement of conquering the Persians. Later Greeks and Romans throughout the Mediterranean world all started to fetishize him and proclaim him to be some sort of godlike successor to Achilles (young, well accomplished, good looking, and most certainly a Greek for living up to the Homeresque glorification of conquerors so endemic to Greek and Roman culture).
Could add a Minoan leader to Greece though. Then we'd have that, Agamemnon to represent the Mycenaean culture, Leonidas and Pericles to represent classical Greece, Alexander to represent Hellenistic Greece, plus Justinian and Basil to represent medieval Greece. Although you could get rid of Basil and replace him with some modern leader of Greece from the turn of the century (though I think you will find much controversy and division among current day Greeks of who would truly be great enough for that representation) then leave Justinian for the medieval representation.