it is possible that lifespan will go up exponentially at some point, through a biological method, but I don't see that happening yet

If you are not that very old you only have to increase your expected lifespan faster than time progresses, that is just change the angle to >1 and you are out of the woods, so to speak. At the moment, my lifespan (based upon the population I belong to) increase with about 3 months per year, if it would increase, I would have a shot at reaching longevity escape velocity.

But we would need an even bigger breakthrough to get to life extension effects to what you're saying, or more likely, several breakthroughs in separate fields. Are we really anywhere near that?

You are quite right, according to SENS there are seven categorise of "damage" that define aging:

From Wikipedia

1. cell loss or atrophy (without replacement)
2. oncogenic nuclear mutations and epimutations,
3. cell senescence (Death-resistant cells),
4. mitochondrial mutations,
5. Intracellular junk or junk inside cells (lysosomal aggregates),
6. extracellular junk or junk outside cells (extracellular aggregates),
7. random extracellular cross-linking.

If you look at every category independently the problem appears rather incremental, it's not very hard for example to imagine that we will have livers made from scratch in the clinic in a decade or two.