Well with a belly like that and expressing milk, I'd say she's in foal and pretty close to foaling.
If she'll let you touch her, have you felt her hind quarters? I'd imagine they're pretty soft by now, around the tailhead, if she is.
I've heard of vets doing an ultrasound on a mini, so I'm not sure why your vet won't. But I agree, if she is you might see the foal before the blood test results.
Good luck! I'm waiting on one myself. Liable to drive me mad lol!