You do a good job of pointing out how the interpersonal and structural issues interrelate - providers can have biases, and then these are exacerbated by a system that doesn't give them enough time or resources to meet the needs of all patients.
I like your idea of a study, but agree it would be expensive. Other options that are less expensive include having "secret shopper" patients of different race/ethnicities do drop in to clinics and have them record whether certain screening tests were mentioned. Alternatively, doing a video patient study, like Schulman, could also work.
And I like the trans-created terminology!