Thought experiment: ultra-fast outward push inside a black hole Suppose I have a classical schwarzchild Black hole $B$ of mass $M$. And consider a spherical-subset (or sub-black-hole if you will) $B'$ (sharing the same singularity and having mass $M'$ (We will bound that $M' >10^{17} \text{grams}$). 
In reading: 
https://en.wikipedia.org/wiki/Hawking_radiation#Black_hole_evaporation
One has that the time to evaporation of the black hole is given by:
$${\displaystyle \tau =8.66\times 10^{-27}\;\left[{\frac {M}{\mathrm {g} }}\right]^{3}\;\mathrm {s} \,.}$$
Now suppose I have an observer $O$ that enters the event horizon of $B$ but has not yet crossed the event horizon of $B'$ (where this horizon is defined as the horizon-that would have existed had all the outer layers of $B$ been removed) . 
Now the radial distance from $O$'s current locatino to the target event horizon can be given by some distance $d$. And the direction vector of $O$ is such that it must have a non-zero component pointing towards the singularity (call the direction S).. 
But suppose $O$ begins to accelerate extremely hard away from this direction towards the singularity. It's not possible of course to actually move away from the singularity but one could reduce the velocity $V_s$ by expending enough energy such that 
$$ \frac{d}{V_S} \ge 8.66\times 10^{-27} \left[{\frac {M'}{\mathrm {g} }}\right]^{3}$$
Then $B'$ would have completely evaporated before $O$ arrived at it. Now $B$ does have a finite amount of time before it will in its entirety evaporate. Yet $O$ appears now to be able to stay INDEFINITELY inside $B$ without reaching the singularity.
So here is my confusion: there are 2 interpretations of what is happening now. Observers on the outside say that $O$ went inside, wasn't seen again, and like all things was ejected as hawking radiation. But $O$ could claim they went inside, somehow managed to avoid the singularity by falling too slowly and now can't escape, but aren't destroyed.
So either: 


*

*In order to avoid this contradiction there has to be a minimum speed that everything must FALL to the center regardless of what they do

*Is it possible for 2 contradictory events to take place and both be valid?
What is the correct deduction here?
 A: No Schwarzschild black holes exist in our universe so the situation you describe cannot arise. A Schwarzschild black hole is time independent, meaning it has to have existed for an infinite time and continue to exist for another infinite time.
This isn't just a bit of quibbling terminology because no true horizon can form in a finite coordinate time, where coordinate time means the time recorded by an observer far (effectively infinitely far) from the mass. However the black hole can evaporate in a finite coordinate time, in effect meaning that a true horizon cannot ever form. This is discussed in Why does Stephen Hawking say black holes don't exist?
A related question has been raised in Does any particle ever reach any singularity inside the black hole? but that has no definitive answer despite one of the answers being from a Nobel prize winner. The impression I get is that we simply don't understand black hole evaporation well enough to give a definitive account of what would happen. Hawking's calculation is semiclassical so it just takes the (nonexistant) Schwarzschild geometry as an existing background. A full treatment would presumably be based on something like the Oppenheimer-Snyder metric and calculate how the Hawking radiation modified its evolution, but I know of no such calculations.
