I divided the vernier scan data into five segments by eta rings, 0 corresponding to the highest abs(eta), 4 corresponding to the lowest.  Each has two rings of trigger patches - one from east and one from west.

In the plots below, black is the cross section from the vernier scan fit, blue and green are the x and y widths from the fit, and red is the background rate from the fit.  The outer eta rings do seem to have higher background, and a higher cross section that may be related to that feature, but the widths, which I'd expected to change if there were different non-gaussian contributions as a function of eta.

I've heard back from Angelika regarding her analysis of the data I sent her - she sees the same nongaussian feature, and has been trying various more complicated models to attempt to get a good fit.