Thank you for the thorough response. Its clear that the answer for perspective attributes = homographies and line = 3D, requiring more in depth math ruling out any simpler resolution. I’ll have to adjust my strategy accordingly.

my *ad-hoc* approach would be to calculate a homography to turn this quadrilateral into a rectangle, define your midpoint in the rectangle, and map that back to the quadrilateral.

This is what I thought. I was hoping to use midpoints in addition to corners for a PnP fx more accurate with a total of 8 not 4. But the homography must be setup first with the 4 corner points to find the other 4 midpoints making a homography with 8 points moot and stuck with 4.