After all the HMO hullabaloo I finally broke down and called my old obgyn who first explained what a chemical pregnancy was and put me on progesterone for my last pregnancy. She was super nice and really sweet and said of course she'd write me a blood test order for hcg and progesterone. She can't do a thyroid panel because it wouldn't be covered but for the beta and p4 she can bill it as "absence of menses" instead of pregnancy so it would be gynecological instead of prenatal.
So I go tomorrow at 9am. Keep your fingers crossed for me.