That's because they often need to form connections with other countries, often foreign powers-- that's why you choose a nobleman or Prince from said country. For example, I believe Belgium in OTL (and Greece ITTL) chose Leopold because of his close ties to both the British Monarchy and people in some German states. For Hungary, likely a Prince from a country that can ally with them against an Austrian reconquest. I would suggest a Hohenzollern, personally.
Unless there is a member of the Prussian branch willing to convert the only option is really Karl Anton (assuming Sigmarignen gets annexed like OTL.) since he is the only one who'd prolly have children at this point, his cousin Konstantin never sired any children, even with his morganatic second wife IOTL.