Thing is, I had more troops than the entire coalition before Russia joined (they were truce-blocked for a while). Still it wouldn't budge.
The biggest hope for my WC attempt (as the Timurids) is that I can use their less passive initial position to abort the two greatest threats I had this run, Russia and the Ottomans.
I know from personal experience (on an older patch, not 1.30), you can perform a no-CB war on Byz while also fighting Ajam for your cores. Keeping everything stable after that isn't the worst thing. At worst, you can leave Byz at low WS but maintain "sieges" on them and come back and finish the war after you've integrated 3 of your vassals.