See above. All four of these countries gained their independence during the 1800s from a controlling authority (Be it Netherlands or the Ottoman Empire), and all four were forced upon/given/settled with German princes as their ruling monarchies. The Belgians got Saxe-Coburg and Gotha relatives of the British monarchy, the Bulgarians got House of Saxe-Coburg and Gotha-Koháry (a cadet branch of the Belgian choice), the Greeks got Gluckenburgs and Romania got Hohellenzorn-Sigmarins.
The Greeks initially wanted a British prince in order to strengthen their ties with that country and gain the Ionian Islands, but instead recieved one Wittlesbach prince who lasted about a decade or three before getting kicked out and replaced with the German-Danish Gluckenburgs. Was it at all a possibility that the Greeks got a British or Russian candidate, or was it seen as a disturbance of the balance of power locally?
And as for the Belgians, they rejected the Netherlander royal family of Orange-Nassau and were initially petitioning for a French king. But that was rejected by everyone who wasn't France, so they went with Leopold I, a relative to Queen Victoria's husband and previously husband to one of her cousins. Was a French candidate truly out of the running, and might an Austrian or other German house been possible?
The Bulgarians had offered the throne of their country to princes from the Caucasus and Denmark and even the King of Romania, but ultimately settled on House Saxe-Coburg and Gotha-Kohary. A Russian candidate was rejected outright (the aid of the Russian Tsar), and the Bulgarians were desperate to avoid Russian influence.
The Romanians had expelled their native ruler Alexander Ioan Cuza due to the failures of his regime, leading in turn to a disintegration of their international standing. Due to the influence of Napoleon III and Romania's strong French relations along with his blood ties to the Prussian royal family, Prince Karl of Hohenzollern-Sigmaringen was chosen as King.
Of the things I could see possibly swapping around or changing, it might be that a French candidate could be directly chosen for Romania (either the Canino branch of the Napoleons or Bourbon or Orleanist) given their proclivities. And a Prussian royal relative on the throne of Belgium doesn't sound too unlikely, though it might upset the Austrians. So perhaps then, the Saxe-Coburg and Gotha find their way to Greece, or even their cousins of the Saxe-Coburg and Gotha-Kohary?
I don't know, this is just a few thoughts I had. Any considerations or suggestions AH might have would be appreciated.