With a little more checking, I have found an at home test that is FDA Authorized and uses RT-PCR through a nasal swab, meeting the exact criteria that SXM is requiring. The test is $120 including shipping both ways and they give you the paperwork to request reimbursement from your insurance company. The turn around time on results is 24-72 hours. I have included a link to their site below. The return shipping to them is next day air, pre-paid by them.

From their website: "Your sample is analyzed in our lab using an extremely accurate RT-PCR based test to confirm the presence of coronavirus (COVID-19). We aim to deliver your result within 24-72 hours of your sample being received in our laboratory."

Lets Get Checked - COVID-19 testing