>>13394039A balloon isn't accelerating away from (Earth?) at a casual pace of 7km/s straight up mate. If you decide to part from a powered vessel at this trajectory your new natural spirit animal is an engine block sized meteor that burns up halfway in Earths troposphere.
The dude you are referring to archived a top speed of 1,357.6 km/h (according to the G), which is the equivalent of 0.37km/s. Just consider the insane slingshot effect mate. The motto is, what goes up, comes down and you have to account for the energy of 7km/s somehow, which translates in a lot of heat for example.
Speaking of slingshots, or Gravity Assist:
Also take into consideration that there's almost no reason for a launchvehicle to go straight up indefinitely, almost all rockets follow a parabola'ish trajectory for a number of reasons.
So if that's up to debate, take that into consideration and the concept of vertically crashing into the atmosphere vs. skipping over it, slowly bleeding speed into heat.
And if your hero has to somehow reappear at the launchsite, I mean then that has to be due to him having plotted a course.
Or you make up some bullshit heat absorbing material to ablate from his shoes and hyper G suits which run on badass 3point landings, I guess