Fortunately, I didn't have to!
I played the save a bit more last night. Almost immediately after I un-paused the game, my ruler died. He was old and I knew it was going to happen soon but that was fast.
Fortunately, I had anticipated my gavelkind problem very well and my main heir inherited the Empire, Kingdom of Hungary, and capital County titles. My only other son got the Kingdom of Wallachia title and a county or two. Fortunately, my first ruler's stewardship score was rather low and I had to be diligent about handing out the fruits of my conquests on a regular basis - that really made the gavelkind succession more manageable.
So my eldest, pagan son becomes king. Surprisingly, not everyone hates his guts... just half of them do. A few bribes, a couple of provoked rebellions and I'm on my way back in the green. Luckily, I took a captive from one of my less compliant dukes and made her my concubine - she was Orthodox and I was able to convert myself in short order.
I'm really glad that happened because my current ruler's brother has HORRIBLE stats and traits.
Of course, now my brother has a claim on the Kingdom of Hungary and the Carpathian Empire. He will have to be dealt with.
In the meanwhile, I am counting the days until I have ruled long enough to change my succession laws to something less chaotic than gavelkind. Any recommendations?