Seems to me two extra hypotheses are worth considering.
1 these things exist in a parallel universe perhaps made of dark matter. We will never touch them in ours. This is unlikely, as they seem to cluster around defense sites.
2 They are images produced by a convergence of several focussed laser beams producing an area of superheated air in a projected pattern. This would enable them to move at any speed including "faster than light".
I also do not rule out entirely observation from the future, although this is real science fiction. Subjective travel into the future is easy, just get yourself frozen. Physical travel into the past is impossible, not least because of the grandfather effect. But our observation of the past is getting better and better, through techniques like DNA analysis, thermoluminscence etc. Perhaps in the far future direct observation of the past will be possible. There may be particular interest in military technologies in the immediate years before the apocalypse.
Remember "nothing is real". It is all made out of atoms with great spaces between them, and quantum links we are only beginning to appreciate.