I ended up actually going back to Karl, but as a cheater; first I gave myself ten million bucks, then I changed my age and cheated my way into immortality (along with Karl's mother and his wife, the ever lovely Desiderata), along with giving him a bit of a stat boost (mostly in learning) and doing the same for his wife. This has proven actually quite fun, in the mold of a kid kicking around a sandbox, so I'm planning on continuing it up to at least the first crusade, if not the whole nine yards. It helps that once I got the HRE out to my intended borders (of basically the WRE minus Britain and Italy from the Papal States southwards) I've been rather passive and mostly watching the AI do stuff as opposed to conquering everything in sight (besides northern Africa, anyway, somewhat out of necessity after one of my vassals started conquering in that direction). My main annoyance is that my vassals in Saxony, Germany, and Bavaria keep trying to nibble away at the Slavic east, which I don't want. Also, my wife (who has become the Queen of Italy) keeps trying to conquer the Papal States, which I also don't want (I want them as a buffer between me and Sicily). I'm just counting the days until I can pass the Vassal Wars Forbidden law, to be honest. The weird thing is that I'd be fine allowing internal wars, I just don't want them conquering to expand my domains, but there's no "Internal Wars Only" law.
I learned from this experience, incidentally, that immortality also preserves a woman's fertility eternally, if she's young enough to have not gone through menopause. Karl and Desiderata have had, like, thirty or forty kids by this point, more or less one every other year or even a bit more frequent. They are randy little rabbits. What makes this even funnier is that Desiderata has been Fat and Obese most of this time. You can connect the dots here, I think
Another thing I learned is that if you somehow contract the kind of disease that doesn't go away on its own as an immortal person, you're pretty much doomed to suffer until God (aka console commands) takes it away for you. Desiderata has repeatedly developed cancer, whereas for Karl's part he's somehow developed Great Pox at least twice despite definitely not sleeping with anyone other than his wife (I mean, like I said, a kid pretty much every other year. Think about it!), who does not have Great Pox. Lunatic and Possessed are also fun, since they're so difficult to get rid of. I really wouldn't want to be immortal without the console, in all honesty, just so I can take care of those kinds of things.