I'm imagining that our intelligence will lead us to an elegant solution that initially appears to work but later proves to have catastrophic unintended side effects. Maybe just copying genes is enough? That brute force approach might be smarter than it appears, given how incredibly common it is in nature. A key thing is that the copies can repair themselves off each other. The more copies that are available, the more robust the system is to error. That's part of why humans have their ribosomal DNA in super high copy number in five psuedo-homologous regions on the short arms of our acrocentric chromosomes. The genome keeps lots of copies of the most important stuff. For humans, cancer wasn't so important, until recently. So we might need to accelerate things and increase our tumor suppressor copy number. It works for people with trisomy-21.
Genetic engineering will be our only hope precisely because modern medicine is disregarding our evolution. Lots of bad mutations are being passed down because we can treat them, which of course allows people to live a good life.
[1] Gene duplication is common in nature, and it's one of the main mechanisms by which new genes with different functions evolve.