You don't have to implement the propagator. You can download it from space-track.org, just like you download TLEs. Go to space-track, click "Help", then click "SGP4", and arrive at https://www.space-track.org/documentation#/sgp4 . From there, pick Windows or Linux, and download compiled shared libraries of the latest SGP4 as released by the US Air Force, complete with wrappers and examples for C, Fortran, Java, Matlab, .Net, and Python.
If all you want is to use SGP4, call those DLLs, and you're done. What Vallado, Kelso, and the others who have contributed to Celestrak over the years want, is to figure out how SGP4 works, which is much harder than just using it. Based on their published error statistics, they're really close, but not quite there. Recently, a friend asked me why he was getting imaginary numbers out of propagating TLEs for some GPS satellites, and this was the answer: he was using a tool other than the official Air Force Space Command product, and when he switched to the real thing, the problem went away.
Note that "Revisiting Spacetrack" and the AIAA 2008-6770 paper have different goals. 6770 is about orbit determination by differential correction, which is much more complicated than just propagation. Propagation means you have a TLE or other representation of the orbit already at hand, and you want to use it to compute position and velocity, or other variables derived from the state, at some list of times. Orbit determination is the reverse process, of starting with a bunch of observations, such as angles, times, and distances, and using those to compute the orbit. A good introductory textbook for orbit determination is Statistical Orbit Determination by Tapley, Schutz, and Born. Vallado and Crawford give a method for making TLEs out of other data, which strikes me as perverse: if you've got a full-blown OD engine, why would you want to produce output in such a crappy form as a TLE? Just stick to coordinates that are unambiguously defined, and stay far away from TEME frames, fictitious mean objects, and the other baggage that comes with the woefully obsolete TLE.