Unfortunately, I don't have the best news to share. Please remember that I'm only the messenger, and not the decision-maker.
Concurrent means two different H1B statuses held at the same time, with two different employers. Concurrent H1B's are not a problem, so long as both the sponsor and the employee can fulfill the requirements of the two employers and the petitions that were approved. But concurrent H1B's is not the issue here. The issue here is who will sponsor one of those H1B's.
Unfortunately, there is no path to sponsorship of the H1B as an independent contractor. So in the case of physicians, physicians must be an employee of a sponsoring employer. Self-employment or independent contractor status are not longer possible at this time. Now if you are employed by an agency who contracts you out, that might be a possibility. In that situation, the agency is the sponsoring employer who would petition for you and contract you out to the hospital. I am not familiar enough with the medical profession to know whether there exist agencies that are contracted to provide medical doctors to hospitals. But that would be the only option for an "independent contractor" situation like yours.
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