I too live the united States, so this is not an option, but even if this testing would be available here, I don’t meet too many of the requirements to make for accurate results.
As for Dr Bianchi’s research, from what she explained to me, she is looking for fetal "free" DNA, and that only stays in the mother’s system for hours, not days or months, so previous pregnancies, miscarriages or even a vanishing twin wouldn’t be of a concern to her.
I was sure she was planning to share the results with the parents. Otherwise, what is there in it that she is expecting will convince us to participate in this study? Is there something she is offering in exchange?