My last jewish playthrough, unmodded, ironman with achievements, went roughly like this:
- Khazars 867 start
- First few decades expansion in the steppes, east caucasus and west turkestan around the khazar sea, or caspian sea as they call it nowadays
- About 60-70 years into the game i and my clans were strong enough, had a land border with the abbasids, and the abbasid caliph was a small and weak kid so i used my once in a lifetime subjugation CB, 2-3 years later i was also the emperor of arabia and owned everything from oman to perm, from crimea to kazakhstan
- 5-10 years later, all muslim rulers were stripped of their titles and i settled down in jerusalem, split away from khazaria, became feudal, as emperor of arabia, which i manually renamed to "judea", also since jerusalem became jewish once i settled there, i could create the kingdom of israel, and start rebuilding the temple
- another couple years later came the test whether i have really earned all this land: a sunni and a shia jihad for arabia (yes it was my fault that the jihads/crusades got unlocked prematurely), and huge sunni revolts at the same time. test was passed.
- after that the game became a bit boring, i am the greatest superpower in the world, i can take on two jihads at the same time, and its not even the year 1000

Now the problems i see here:
- what do i need the kingdom of israel for, other than the steam achievement? by the time i am able to create it, i already have at least 1 other king title or even better, an emperor title
- the kingdom of israel is very special in the game - it is the only kingdom for which the de jure drifting rules do not apply
- if if was possible to create the kingdom of israel, and survive to the end of the game, not as the king of somewhere and israel, not as the emperor of something and israel, but only as the king of israel - what would need to happen for this to be possible? as things are, if theres just one tiny jewish area in the middle of muslims and christians, who both even have a high chance of picking jerusalem/israel as their crusade/jihad targets, then the chances of surviving are really small, then there need to be more jewish states who can jump in and help, preferably somewhere close and not on the other side of the map
- currently there are 2 "official" ways - khazars or semien, as khazars you need to become a world superpower to be able to invade all the way up to israel and stay there and survive, with semien its the same only the whole process can take a few hundred years longer than with the khazars
- other unofficial ways are, play or create a non-jewish superpower, like byz or HRE, teach your ruler jewish religion, invade the middle east and create israel, at the end of the day its the same "gamey" strategy that requires the player to become a superpower first before creating the kingdom

My suggestions for this mod:
- make the kingdom of israel a proper kingdom with "equal rights" - allow duchies to de-jure drift into israel
- change e_arabia - if it is held by a jew, replace it with another empire, something like e_jewish, give e_jewish a proper jewish color (not green) and a proper flag
- make it possible to become _only_ the king of israel and survive - this is probably the most difficult part as i dont even have an idea how we could do this, hopefully someone else is smarter than i am

Would be interesting to hear from others, what is your experience with k_israel, have you ever managed to become the king and only the king of israel?