But not so radical that we won't be "recognizably" human.
Consider Google glass, and people with artificial limbs, hearing aids, etc. Stephen Hawking communicates trough a machine. Technically, we are already radically altering ourselves. Do we call those users not recognizably human? No, we call them glassholes ;p
Artificial limbs have been around for a long time, but the first using signals from nerves date from the mid 90s according to Wikipedia. Glancing at Wikipedia, Hawking's speech synthesizer was in use since around 1985. Google Glass entered the market this year. Technically, we are already radically altering ourselves over the past few decades.
Biologically, they may deserve a new scientific name (no longer homo sapiens), but they would still be considered human, and refer to themselves as humans in everyday conversations, while the rest of us may be the ones who get a new label in the variation of "old" humans.
Unless it doesn't happen that way, of course.
Actually, it was labor being too expensive that created the incentive for machines and automation and AI to be created in the first place. To compete with machines, labor doesn't need to augment themselves. They just need to lower their price.
Horse-drawn wagons and chariots created the need for roads, but they aren't on the roads now.
This is one of the great misconceptions many first worlders have. People only think about the cost, as opposed to getting value for their buck. For example, what good is going to a more expensive school when it lands you the same job as somebody with a degree from a less known but cheaper school, or no degree at all?
OTOH, if it's not that way, then your argument wouldn't hold.
To compete with machines, labor doesn't need to augment themselves. They just need to lower their price.
Many if not most people choose to work more than 40 hours of work a week. They could choose to work less and earn less. Just because someone could choose to be unaugmented, doesn't mean they will choose to do so due to the compromises involved.