Sure, somehow I'm worth ~$140k/yr (plus benefits, etc) to my current employer as a FTE (who bills me out at a much higher rate to our customers, I'm sure), but I'm in govt contracting - it's a different world.

How to find private sector clients willing to pay good rates? I have no idea.

It's sometimes possible for a small business (like a single-member LLC) to bid on government contracts. You can try to cut out the middleman.

My personal style is to avoid getting into bidding contests. I've invested years into building my personal network. That means enthusiastically following up with strangers that I meet to turn them into acquaintances and semi-friends. It's exhausting, but has paid off. For example, sometimes I get a call out of the blue from someone I haven't spoken to in 3 years asking me to help with a project.

Don't expect people to sign contracts right away. Give them time. Years, perhaps. Just put the word out there that you're skilled and available for work.

Edit: Also, you need a specialty that allows you to accomplish something useful in a few months by yourself.