Circumventing third party recruiters?

I recently got approached by a third party recruiter about a role at a well established tech company. I went through the interview processes with the recruiter and he was ready to send me onto the company for further interviews, but stopped short once he realized that I would need visa sponsorship (American in Australia). He insists that there is no way that the company would be willing to consider sponsoring for a 12-month contract position.

I then applied directly on the company's website for a similar role, but it was not listed as a contract position. Now I'm wondering if 1) this is the same position that I was contacted for or 2) this is a similar position, but the full time version. Which leads me to wonder if I have a higher chance of getting hired and sponsored if I get noticed by the internal recruitment team.

Of note: the company is known to sponsor a great deal of foreign talent.

Does anyone else have experience circumventing third party recruiters? Have you ever gotten a job that a third party recruiter rejected you for by applying directly with the company?