I haven't seen the film so can't comment on the effectiveness of the "docking waltz". But there is a big difference between 2001 and First Man (which should really be called "Second Man", but ya know American ego and all) 2001 was fictional while First (Second) Man is supposed to be biographical. I also question doing a homage to a fictional movie in a biographical film. It sounds like so many films nowadays which are about style over substance.
Oh, I don't know Sol. They did go for a spin with the Agena, after all.
I should really have my coffee before commenting. I criticized the movies title thinking the film was about the first man in space, not the first man on the moon. Sleep brain fart.