Question raised by that briefing: If they have taken steps against surveillance from the balloon, but LEO satellites provide similar or better coverage then doesn't that run a risk of creating an observable delta? OTOH, It can certainly be a good time for a solid misinformation plan. Are there any secret carrot farms now laid out in the area? Lots of radio chatter concerning Christopher Robin's woodland friend?
The AF is not saying the altitude, but a couple of people with theodolites or sextants could get some known separation to find that out, most easily around dawn or dusk. About 2 -5 miles ought to be enough for non-precision equipment to manage a +/-5% estimate (any school children in Montana looking for a project?) Decent astronomical telescopes should have sufficient precision to get better results. Don't forget to correct for curvature of the Earth!