I'm guessing this response is coming way to late, but just in case it might be helpful to someone else who sees this thread, I'd submit the tax paid under their LLC. In the first or second page when it asks for the sponsors name, it also asks for the business or organization that will contribute to sponsoring the beneficiary. If they are using the income from their LLC for the sponsorship, I'd include that there.
However, I also agree with the person above, so hopefully ya'll already heard back and it was positive! Best of luck!