Is there a Byzantine strategy posted before ?
I did it on 3000 bc. 600 ac is far more difficult.
Rolling a good start is a great first step, on my game i started with constatinopolis+athens+sur+jerusalem+3 cities in egypt, lots of wonders and plenty of legions. Something i didn't do but is good is switch to militia, you won't be hiring mercs before 1000 ac, and most of the battles will take place in your borders.
By the time arabs start attacking, you need engineering, plenty of barracks and walls in at least sur+jerusalem. Leave a skeleton guard on egypt, expendable troops on jerusalem, and legions/cataphracts on Sur. Sur doesn't flip, so in theory the troops there should not desert you. Also, razing babylon before it flips to the arabs REALLY helps.
Raise castles asap on sur+jerusalem, whip if necessary, and whip pikes whenever they are most needed. (except constatinopolis). The arabs will send several SoD's to the levant, and leave egypt alone. It's a fierce battle, but you should not yield a single city to them. I managed to do it while building the AP on constantinopolis.
If you withstood against the arabs, the rest of the game is much easier. Get civil service for absolutism, zero your science and go for GMs, this should be enough to get the gold UHV. With 5000 gold to burn on mercs, the seljuks and turks should present little problem. I was also expecting an egyptian respawn, but they didn't come, i guess denying egypt to the arabs prevents their respawn.
Unless you abused whipping constatinopolis, you should have no difficulty getting the pop UHV, i had a size 22 city by 1000ac. If you need culture, remember researching patronage nets you a free GA, i needed it.