Following the advice of several folks here who early this summer suggested I could improve the trigger pull and let-off on my Shield by (1) polishing the offending parts and (2) installing the Apex kit, I ended up doing both.
The little .40 shoots better than I can hold it.
First, got the sight re-centered, even though it was pretty close anyway.
Here is the best group that I had after it was centered. The height is fixed, can't adjust that, and since my hands are not as steady as a machine rest, I guess this is about as good as I can get it.
15 feet, resting on sandbags: Final 5-round group = 3/4-inch x 3/4-inch edge-to-edge, Centered 1-inch above nominal point-of-aim at the crossing line. [I say "nominal" because my prescription doesn't sharpen up the front sight very well.]