The death of humanity as a species is a given.
Time is the only variable. You think our technology will extend that time - I do not. Current science and cosmology provide no practical way to expand even to the most nearby (and very hostil) worlds, and finding another that is actually habitable is entirely out of the question.
There may be a way out of here but it's not through technology. You'd need to come up with a whole new definition of how the universe works and demonstrate that it works that way.
The massive expenditure and depletion of resources you propose to set up one or two doomed colonies would be far better spent fixing problems here, and that would also avoid the severe damage to the upper atmosphere your project would cause.
As for your small tribes and island peoples - point me to one where power struggles and fits of jealousy were/are not a feature. They live in a highly resiliant environment that can absorb damage done, and for those who can't get along, there's the option of leaving. In your colony just one person with a grudge and suicidal frame of mind could easily destroy the entire colony.
And even if it did survive into a second or third generation, expecting the people there to adhere faithfully to your plan is simply absurd. They will have their own agenda.
Living as a tribe of Siberian nomads would be far richer and less dehumanizing than living in your underground moon base would be anyway.
