Let's start here: "Is there an option that my client 1099d me as their contracted employee"

If you intend to do this for your profession, never state that again. There is No Such Thing as "1099 employee."

A 1099 is how someone would Report that they paid you $600 or more for their Business needs, and you performed a service to their business, with you acting on your own behalf as your own business. Not "employee" for the purposes of 1099 reporting.

And even if you made $23million, if no one client pays you $600 or more, there is no 1099 ever needed.

I hope that helps you see how this has nothing to do with what you asked, and it was also not phrased properly for any relationship that exists.

Here is an IRS resource for Forms:

https://www.irs.gov/e-file-providers/reporting-agent-technical-fact-sheet