Until and unless it applies to me I haven't got the energy to investigate what alternative methods exist for gaining the right to reside in Greece.
I know that one method is with inward investment of €250,000, e.g. buying a property of that value or above, but that seems limited for 5 years with no clear picture of what happens then.
There is some other information here
, if you are self supporting and here
if you intend to work. It looks like for the independent means route you at least need an income of €2,000 per month or €24,000 in a bank account and medical insurance. It is also a complicated process. You apply for a Visa before coming to Greece. When you get here you apply for a residence permit. You then have to renew it after one year. I have no idea what restrictions apply that might stop you being granted it.
There does not seem to be any method other than EU membership, plus countries like Norway, Iceland etc that have rights through EFTA or similar, that gives you an indefinite right to reside but I could be wrong.