an LLC, of which I am a limited partner with .0001% interest,
I'm a sol prop/independent contractor.
Unfortunately, no, you are not a Sole Proprietor/Independent Contractor. At least not for this business. You are a Partner.
And even more unfortunately you connected yourself with the messed up business. They are claiming you are a "limited" partner, yet at the same time you are working for the company. Those are generally opposites.
Does the agreement with the Partnership state that YOU must pay for all expense out of your own pocket?