AHC: Preserve the Greek Monarchy

Because I've been reading craploads of Greek history lately and it's turned me into a Philhellene:

With a POD between 1949 and April 21st 1967, ensure that the Greek monarchy remains to present day. Bonus if you accomplish this with minimal bloodshed and political thuggery.
 
All it would take would be for Constantine II to grow a backbone and refuse to cooperate with the colonels even more so if he takes steps to try and end the coup. Really though all it would likely take would be for him to just keep his head down and do the the bare minimum to assist the junta and he'd probably manage to keep his throne even after it falls.
 
I don't really know if that alone would do it. After the Apostasia in 1965 he pissed off a lot of influential people, namely the Papandreous, perhaps that injustice combined with any perceived tolerance of the Colonels would be enough to make them call for his throne after 1974. You'd also have to butterfly Queen Fredrika out of the scene to get Constantine to grow a pair because she pretty much ran him like she ran (to a much lesser extent) her husband the late King Paul.
 
I don't really know if that alone would do it. After the Apostasia in 1965 he pissed off a lot of influential people, namely the Papandreous, perhaps that injustice combined with any perceived tolerance of the Colonels would be enough to make them call for his throne after 1974. You'd also have to butterfly Queen Fredrika out of the scene to get Constantine to grow a pair because she pretty much ran him like she ran (to a much lesser extent) her husband the late King Paul.
What if she doesn't outlive Paul, or not by much?
 
That could do it. Ioannis Katris in his book about the era also suggests that Fredrika could've been pensioned off to her vast estate in Austria, which would remove her from the direct picture.
 
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