I don't see it as a major issue at the moment. First off, this is for the commercial aspect, not the recreational end.
Second - you can appeal the no-fly list. There are lots of people on the list for no good reason, some for disagreeing with the government, some because of relatives ( one person had a distant relative in the IRA ) and yet, some people are removed for no known reason even though they are the issue. ( hint Orlando ) So check to see if you are, then if you are, appeal. My guess is that if that youthful indiscretion did not involve a gun, or explosives, you are probably fine.
I once worked with WHCA for years and found that the secret service is great to work with on any issues. So is the Pentagon.
The toughest background check I ever went through was by the mob. I was in tech theater and ran a show for Frank and his "security" team was very thorough, hence the mob statement. Every tech backstage at any of his shows got that check.