Can you show us the video? What is your difination of skipping off the atmosphere? 100km Karman line? Skipping off atmoshpere involves 2nd reentry assuming the
warhead ever left atmoshipere (it doesn't see below). So far the only two known demonstrations of such maneuver were China's Chang'e-5 and 6 capsules returning from the moon by bouncing off above 100km with a 2nd reentry and remained controllable. U.S. has never demonstrated that capability, neither NASA nor LM itself (orion spacecraft). If LM did make a video as you said, it is just a wet dream.
Real study has shown that prefered altitude to begin glide is well below 80km (well within atomeshpere) for a range that is much longer than LRHW. You should know that NOBODY want to skip off atmoshpere, it has no benifit in extending the range because there is nothing for the warhead to gain lift.
Have you ever read any study of various trajectories of HGV? Or saw any data diagrams other than some promo CGI video?
All your arguments here are based on "probably", "may be", "if I had to guess", what is this? Is this what you call "substance"? I will remind you what was said by yourself in post
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