NASA funded a study that suggested they start with a jet going mach 10, or 3.5 km/s. The fastest a person has ever gone is mach 6.7 or 2.02km/s.

In a jet. In a rocket, just the ISS is going at >7km/s, so obviously it's routine. A (scram)jet would be nicer from a fuel point of view, but you don't need it. In any case, to get to double the velocity with the same acceleration, you just accelerate twice as long - space is always big enough for a pure rocket-type craft (beamed power or gun-type are a different matter).

When it comes to the skyhooks themselves, the study you're thinking of gave a spread of different accelerations for the designs, from <1 G to quite heavy (but manageable for a trained professional).