I have not come across one that will control either. Has anyone else?
I don't think I have. It's like the DC suppliers liked the name SSR and wanted to use it for their product. Most DC SSR I've seen use mosfet switching elements and of course most AC SSR use triacs as the switching element.
I guess it would be possible to design a AC/DC SSR but it would most likely cost more then the present AC or DC SSRs for the same current/voltage ratings.
Lefty