OK, it's really kind of irritating just how bad a rap Franz Josef tends to get on this site. Yes the man was a dyed in the wool, unapologetic conservative more at home with soldiers than politicians, but the man was no idiot. He steered his Empire through sixty-eight years of deep uncertainty, political changes and two major military defeats without once being in danger of a revolution or dissolution ( FJ can't be blamed for 1848 and it's aftermath while, despite what people believe, the Empire wasn't in danger of collapsing in the aftermath of the Seven Weeks' War). Despite the many nationalities the Austrian Empire had, under Franz Joseph it was a bastion of stability for Europe. Hell for the last 49 years of his reign he ruled as a constitutional monarch, never attempting to do anything against the constitution, and even intervened behind the scenes to ensure the passage of universal suffrage in 1906. That the Empire dissolved within two years cannot be blamed on the Emperor, nor really can World War I. Ultimately
As to the idea in question, I don't think that any of Franz Joseph's brothers could do a better job. Despite our site's tendency to hold him up as the would-be savior of Austria, Maximilian doesn't fill me with confidence. He was a liberal but hopelessly naive. While his two years in Lombardy-Venetia seemed to be successful, it's his Mexican reign that really makes me apprehensive. "To liberal for the conservatives and not liberal enough for the liberals" was a (paraphrased) description of him in Mexico. I just have the feeling that he would try to please everyone and ultimately piss off everyone. Don't know much about Karl Ludwig or Ludwig Viktor so I'm reserving judgement on them.