From the arty falling even though you make it to the gate, to the gate guards' backs to you and not interacting once you arrive, this has stopped my gameplay dead in its tracks for about 5 months now. Bethesda has sent out a lot of bugs affecting gameplay, but you MUST complete the Nellis AFB missions to advance the game.

So . . . when is a patch addressing the arty and guards at Nellis going to be released?

I'm going to guess that probably this was broken at another time by choices you made (not saying it's your fault, but that a series of things that happened while you were playing caused this to glitch), and you're going to have to restart with the new patches to fix it. I doubt they are going to be releasing any patches this late in the game to fix broken quests (especially when they're not broken for everyone).