Kenny,
I'll give you my opinion on the matter, but I hope others post theirs, as there are certainly many, many other viewpoints.
The U-2 guys that have gone in to the aerospace sector were pretty well networked, for the most part. While some of that was through the U-2 Brotherhood, much of it was also because they built relationships with various the people from those companies while they were on active duty. They would go TDY to conferences, site visits, etc... and made the effort to stay with the entire group, rather than bolt and do the "aircrew only" bar scene once the meetings ended. For example, one friend of mine became a trusted agent and social friend to a couple of Flag Officers, an Under Secretary, and and some other heavy hitters you would know from recent news events. I have very little first hand knowledge, but I assume the same opportunities exist within your community.
LinkedIn: I built a profile years ago, but have never used it. I'm sure there are success stories out there, but the positions I were offered were not something that I could imagine happening on LinkedIn.
The Executive Director position I had from 2014-2016 was purely a result of meeting some CEO's and entrepreneurs at Oshkosh, and spending many hours engaged with them on a personal level for a couple of years.
One interesting "networking" thing that happened was at Oshkosh in 2003 or '04. Two of us flew a Beale T-38 there for static. Met and spent quality time with some people from Virgin. A couple of nights later, I'm at a small, private house party in Oshkosh with about 30 people. It wasn't until we walked out to the pool area that we realized Richard Branson was hosting the party. Too bad I had no aspirations to move to the UK or Mojave.
In summary, Kenny, I don't think the positions you would want will easily materialize through job postings. But that's just my opinion, since I have no direct experience with social media job hunting.