Most of the bullet points for Documents Required in you link actually say "not required for freelance" but then I see:
"Proof of a secure livelihood must also include sufficient health insurance."
Did you have to show a current consulting contract?
Do you have to show that you are currently contracting for a company via invoices?
If so does that consulting contract or invoices have to be from a German company or could it for a company in the US?
Is it possible to contact you off list?