Okay so not many peacefull options I hear? That might actually be the only little thing I dislike about VP...
Btw with peacefull I do aggressive wars it doesn't mean I'm not willing to defend what is mine!
I would love to hear more about that Byzantium diplomatic game. I have no idea what that would look like. I always considered Byzantium rather weak with only 1 extra belief instead of a real UA. But than again that's only theorycrafting and often Civs in VP are much stronger than expected when you actually play them...
For diplomatic Byzantium, key beliefs would probably something along the lines of Universalism (you can't found a religion and start spreading super quickly like Ethiopia or Mayans, so being able to erode existing pressure is key to getting your religion a strong foothold, this also allows you to save your Prophets for Holy Sites) and maybe the Reformation belief that gets you votes from Landmarks and Holy Sites, don't remember the name offhand. Spread your religion aggressively to City-States and any Civ that hasn't founded their own religion, get Borobudur and Hagia Sophia if possible to boost your spreading abilities. You can also spread to other civs that have founded their own religion and give you OB, this will make them mad but it can eventually leave them not able to really recover religion-wise.
Try not to use your ability to found after all religions are founded, one more civ with a religion means one less civ you can easily convert. Follower beliefs and Pantheon shouldn't matter too much, Churches are the best building for pressure but I'm not sure how much of a difference they make offhand versus the others.
If you have enough cities, Orthodoxy has the potential to put a lot of passive pressure on other competing religions or wipe them out entirely. Build roads between all your cities and going out towards the cities you want to convert, this should increase the passive pressure. Orthodoxy and Byzantium's UB both increase pressure from Trade Routes and I believe Trade Route pressure is based on Faith generation in the originating city so your trade routes should deliver some pretty hefty pressure as well. Orthodoxy isn't as worth taking if you're staying small though.
Statecraft vs Fealty is a tough decision, Fealty will help you spread a lot more but Palace of Westminister is too good if you're going for a Diplomatic victory.
I haven't played Byzantium yet but I'm planning on doing something along these lines in my next game maybe and I did something vaguely similar with Ethiopia in the past.