None of the gret powers would have allowed for Crown Prince Rudolph to be greek king. First off, he was a child, second, Russian interests in the area, they would not have allowed a future rival Austrian Emperor to rule a country so near their interests in the Bosphorus, and the British and French are fine with Austrian power keeping Prussia in check in Central Europe, or Russia in Balkans, but they don't want Austria too close to the Mediterranean.
Maximilian would have been disqualified as you say because he was at that time the second in line to his brother Francis Joseph's throne in Austria. Ernest II, was Queen Victoria's brother-in law, (Prince Albert's only brother) so his close relations to Britain may not have garnered enough support.
Ernest II was also an avowed German Nationalist and I don't think he wanted to remove himself from the scene in Germany. The members of the family had an overblown opinion of their influence in Germany since Ernest II was not just close relations with the British Monarchy, but he was the paternal uncle of the Kaiser's mother, (Vicky) the Empress Frederick, and the great-uncle of Wilhelm II. I believe he served alongside the Prussians in their wars for unification.
They are too close to the throne of the Austrian Empire. If the goal was to be sure they were not from the dynasties of the great powers of Europe then I would think any members of the Romanovs, Hapsburgs, Hohenzollerns, Saxe-Coburg-Gothas, (British line), or even the Bonaparte's who were in power in France at the time, or the Savoy's in Italy who were at that time recently united, will not be considered. A minor line may be considered, but the Danish Royal family members fit a great compromise as they were an accepted Royal line, and from a nation with little or not influence in the area. Also any member of the Orleanist-Bourbons descended from King Louis Philippe I would most likely be vetoed by Napoleon III.
Denmark, Sweden, Belgium, the Netherlands, minor German kingdoms, Saxony, Wurtemburg, Bavaria, Spain, Portugal. Minor kingdoms with possible princes who could sit on the Greek throne.
But in 1863 the powers at that time agreed that the candidate should not be among their Royal Hoses. Italy albeit inly a new power, would have fallen into that carry. What happens later in the 1870's was another time and issue. (Spanish throne.).
