This grandmother's puzzle

I’ve been fiddling around for years and years trying to do a paper foundation pieced Grandmother’s Flower Garden pattern by machine. The usual method is to join the hexagons by hand using the English paper piecing method, but I keep thinking there must be a way to foundation piece (paper piece) the design.
Click on the photo to see the whole quilt from the University of Wisconsin’s collection.
Several quilters have devised methods of sewing the hexagons by machine. Quilters’ Cache has a method using strips, and Sharon Schamber has figured out how to machine sew the hexagons.

These honeycomb or mosaic quilts have been around for well over 100 years. I suppose quilters have been trying to figure out new methods to create them for a long time too. It’s rather like those unsolvable mathematical problems (The Goldbach conjecture, The Riemann hypothesis, The twin prime conjecture) that mathematicians have been working on for years.

I want to do the hexagons on foundations in circles. So far I’ve had many failures. Ideas come to me during the middle of the night, but when I try them out the next day they just don’t work.

Yesterday, I came close to a method that might work. See this picture:

I still have to tackle the outer circle edge, but it’s looking promising. So I’ll settle back down at my machine and keep on trying.