Be slightly aggressive
If you're a decently skilled employee in the government contracting world, there is no reason you shouldn't be able to go 1099.
The main differentiator I've seen between people who claim they want to go 1099 and the people that actually do it, are that the people who pull it off are just a little more aggressive (assuming they are equally skilled, in desirable fields, etc.).
The successful ones "pester" their network a bit more, negotiate a bit harder, and push to go 1099 for longer.
Being a little more aggressive doesn't come naturally to most people. That's okay. What matters is that you do it, now how you feel about it. It will become more natural over time.
I'm not trying to push some motivational nonsense about forcing yourself to work harder. It's just a reality that the longer and more forceful you try to make something happen, the more likely it will happen.
You won't be able to do it if you don't truly want it. But if you do want it, you might think you're doing something wrong when it doesn't happen immediately and then give up.
That's not the case. It just takes more time and effort and something will give.
So if you want to go 1099, give it a little more oomph and a little more time.
If you do, the odds of you getting your first 1099 gig go way up.
Want the full playbook? Check out Going 1099.