The most recent adventure was in Winter 1231, but I'm expecting us to move on a few seasons before the next adventure. I don't think there's any reason for you to need to anchor your characters to 1220 (unless they need to be for backstory reasons) - feel free to have your guantlet om whatever year works best for you.
My read of the Longevity ritual rules is that you can sometimes changes the type of Vis you use (and Animal would be reasonable for a Bjornaer), but not the Arts used in the lab total.
I assume you're taking the second option? I generally assume a Longevity ritual with a lab total of 50 is reasonably easily available. Houses of Hermes: True Lineages suggests that House Mercere generally pays 1 pawn per 10 levels of lab total plus costs for longevity rituals - that's implied to be relatively generous but is probably a sensible starting point?
Realms of Power: The Divine has this to say on Jews in Constantinople:
Though tolerated, Jews in the Byzantine Empire suffer a number of restrictions. They may not build new synagogues, nor may they read the scriptures in Hebrew. They are also prohibited from serving in any position of government. But beyond these restrictions, the authority of their courts is respected, such synagogues as exist enjoy legal protection, and they are free to follow any craft, trade, or profession.
The large Jewish community of Constantinople suffered greatly after the city’s fall in 1204. Many were either killed or driven from the city, their properties burned or stolen. The population is much smaller in 1220 and, given the restrictions on rebuilding their synagogues, most must worship within their homes.
So it looks like Jewish soldiers could have been a thing in Constantinople in 1204, and would probably have had good reason to leave after it. That was 27 years ago now, though, so they'd be getting a bit long in the tooth.