"the first person to live to 1,000 might be 60 already"
doubtful and damn it either way that leaves me out.
I think it will happen but I can see huge social problems as to who gets the treatments. Imagine a world with clinical immortality possible but only to select individuals. The science may be available long before it is made available to the mass of humanity.
The nature of time will change completely. Even normal aging changes the perception of time as each future increment becomes smaller in relation to total life span.
I have always believed this is the way we will negate the FTL problem.