should have done or could do?

[Aivaras]

Could you, please, explain whether both could and should have are possible in the following gap (Is there any difference? What kind of?):
“They sometimes think that they shouldn’t have left London but they never really regret about their decision. ‘I think we _________ (move) years ago. We wasted so much valuable time’.”

[rancher247]

Take a look at this website; it may be helpful.
Learning English | BBC World Service
I think it should be "should have moved".