This effort would need an analogous long term funding source.No need to re-invent the wheel: turn the problem over to the religious.
The Roman Catholics has a long organizational history, millions of adherents, a large and functional bureaucracy, familiarity with generations-long projects.
Also, they speak Latin which will jazz things up.
I suppose Rome needs a reason _why_ to pursue this.
- Long-term people will be in space. They'll need ministry.
- If you're looking for the ultimate in isolation from wordly concerns for your religious, you can't beat the Oort Cloud.