Develop scarce skills
I was able to go 1099 because I was one of the few people at my company that had a clearance AND could use Excel to do data analysis.
On my recent projects, I was only valuable because I was one of the few people that could build Tableau dashboards, a skill I learned on the job.
One of the ways to be successful in the 1099 space is to be one of the few people on your project who can perform an important skill or do something valuable.
It doesn't mean you have be the best in the world, you just have to be better than the group your client oversees.
It also doesn't mean you have to be the best at the thing you were technically hired to do. If you were hired to do data analysis but the team is sucky about project management and "managing up," you can fill in those gaps and become valuable that way.
Find some way to develop the skill that is missing and valued on your projects and you will be seen as indispensable.
Want the full playbook? Check out Going 1099.