Didn't want to argue in bad faith, but, since your assumption was constant force acting upon a known mass, moving it by a known distance, in a known (which was implied "universal") time-frame; you are already saying that Sasuke was moving at FTL for a part of the distance (because again, this part of the calc was given a classical treatment)
Your average speed is 0.86..c, but 2nd end of your calc (which uses Relativistic kinetic energy) suggests it reached 0.86..c
after traveling 0.97m (or whatever) due to the constant force acting upon it. Which again, not the way.
You can actually find a Force expression for mass m moving x(t) or lets say (distance D in this case=0.974m), in a time t as measured by observer lets say (Tau in this case since I had to switch variables in middle=3.74966071e-9s), in 1-D, due to a constant force F.
(Tau here is
not the proper time btw)
The expression is F = 2*D*M/(T^2-(D/c)^2) and inserting above values you get
7.56*10^17N which is even greater than what you got (expected)
And you can even find the real final speed by utilizing the expression for v you already got above and substituting F in it.
F=2Dmc^2/((cT)^2-D^2), v=2TDc^2/((cT)^2-D^2)/sqrt(1+(2DTc/((cT)^2-D^2)))^2), v=2TDc^2/sqrt(((cT)^2-D^2)^2+(2DTc)^2), v=2TDc^2/((cT)^2+D^2)
Which is 2.967385951736*10^8 m/s which is about 0.9898c