Ugh patriarchs. Whats the benefit of going theocracies as Orthodox if you can't use them to prestige a relative into the college of cardinals.
I would have kept Antioch the county for the monies. I love Antioch especially if you can get to it before some stupid AI fills it with something other then cities.
First I would auto do the baronies.
Then I would pick one duchy to maybe give to a male preferably non claimaint dynasty member. Either the bigger one or Jerusalem, actual duke or strategos is up to you. Often in the Byzantine Empire I did like to make my family special by actually making them dukes but this tactic could be debated. Either way I would give him at least 2 or 3 counties in his duchy.
After that I would give every other province to a single count. Remembering that it is cheaper to invite holy men with piety or uplift auto-generated barons then it is to invite nobles to court, if you run out of potential people. If you really want to min-max make them high stewardship counts.
Then optionally make one of those counts a strategos of his duchy(not one in your relative's duchy). This may help your new Exarch deal with potential vassal limits if he has them this is dependent on many factors.
And then yes make your relative the Exarch. Because even relatives misbehave and we like to keep options open when he dies.
This leaves you with one vassal who loves you, is of your dynasty, and with his 2-3 counties has at least a strong, but not too strong, core. So that he might deal with his vassal counts well. His vassal counts who with one county each will promote culture shift quicker then one guy owning multiple counties.
Thats how I do it usually. Strong family core with at lest a few counties, a duchy and the kingdom. And then vassal counts for culture conversion as their vassal count allows.