My first campaign as Pontos on VH/M wasn't as difficult as you describe.

Disband your unit of cavalry.

The AS will attack your capital if anything else. A couple units of Phalanxe and your General is MORE than enough to defend against almost anything they send at you. Do you auto-calc or fight your own battles? If you fight your own battles, set up your Phalanxe in your town in a narrow alley and watch the enemy armies crumble on your spears.

There is NO need to build any baracks in your capital this early in the game. What's the point? Your economy is in shambles, having access to more expensive units is completely useless if you cannot yet afford them! Instead focus on building economy based buildings (Ports,Roads,Market,etc) One of the first things I do is build a road, allows you to move more efficiently through your growing empire.

While your couple units of Phalanxe and General is protecting your capital, have another army moving through and capturing what you can. I ussually take Sinope and Ankyra. Around this time AS tends to betray me, and then I move this army West through Anatolia and take out all the remaining AS settlements. Once you take all the AS settlements to your west, it's much easier defending and your economy will be rolling.

Don't worry about Eperius. You will be at war with them once they attack Byzantium. For this reason, I don't bother capturing Byzantium until my economy and military is up and standing. Instead, wait for Eperius to capturing Byzantium, and then send a diplomat and establish peace and trade with them.

You are sending your diplomats throughout Greece and getting Trade rights correct? Especially important to do this because you will be at war with KH for attacking Sinope, and you need to secure peace/trade with them asap.