Ultimately, I think that if we want to extend life indefinitely, we'll need a strategy that involves replacing organs, replacing brain tissue, and maybe replacing most of the human body. You might be able to boost someone's life span by a few years with stem cells and such, but that's just patching the binary like you said. It's like repairing a home. You can patch drywall, but eventually, to fix a very old house, you might have to rip everything open and replace most of the materials. At some point it's easier to rebuild parts of the house than to keep patching.
IMO, we should be harnessing the fact that nature is very good at growing new healthy tissue. There has to be a way to coax stem cells into growing a new heart, a new liver, or a new arm. We ought to figure out how to do that. Then we could potentially grow you a new liver in a vat based on your own stem cells in a matter of months. We might even be able to automate surgeries such as liver replacement. That kind of technology seems like it should be feasible within 20-30 years with targeted research.
And unless you can figure out why cells age, you can't build new humans who are immune to senescence either.
Defeating the aging process is critical to solving both problems.
The only roadblock to doing this right now is access to training data.
Death sucks, but I’m not sure indefinite life extension is a great idea for humanity at large.