Epsilon Totality-OOE / Eclipsing object shape
Here is the graph I have not been able to attach to my comment to your blog on the eclipsing object image.
It seems the right section of the object, just after ingress, is thicker than the center and left section ? If it's right this well explain the strange shape of the light curve during the totality.
OOE excluded, we have first a progressive dimming and about at the third a 0.12 mag step up of the brightness and then a more or less flat section (with a slow dimming) At end the recent abrupt dimming is well visible.
I think this fits your image well.