I haven't seen anything quite like that before...nutritional deficiency of some kind maybe?

Have you sprayed any herbicide or Round-Up in the vicinity? Or maybe your neighbor has? Sure looks like herbicide damage to me. Not sure of the long-term prognosis.

I actually sprayed some herbicide, but I thought I was careful to keep it contained. No other plants were damaged. Not even any of my roses, which tend to look virused with herbicide contact. I guess it's still a possibility. It just started growing 2 inflos, too, which I thought I wouldn't see this year, so that's a complete surprise, especially after the freak show it put out.

I'd be 95% sure it's from your spraying. Different plants have different sensitivities to herbicides. Sometimes it doesn't take much more than fumes travelling on the breeze to affect some plants. Consider how well plumeria do with foliar fertilizers -- they can take up a lot of chemicals from their leaves.

I agree that is the most likely issue. I would remove them.