Are you playing a mod? I've never had a single King assassinated, and only very rarely lose anyone before old age takes them. I normally play m/vh, but even in my England vh/vh game (1.2, but awhile ago) I don't recall any meaningful number of attempts on my king's lives.

Interesting situation. With guns pushing back the Mongols shouldn't be too hard, but I've never seen so large a Timurid empire (Probably because the game rarely goes on so long). Good luck!