Hi, I'm not really qualified to comment on your research, so feel free to just close this issue if responding will waste your time.

I was looking through the CSV of your data and found it peculiar that instead of calculating a probability for each bin independently according to your model, you seem to have used control points, and interpolated linearly between them. (This for the only subset of data I looked at, QF4 from 2020-03-30.)

The probably curve has long stretches of constant slope for some multiple of 10 bins, which is quite a lot of the probability space at the low end:

I wonder if there are limits on your model that prevent determining a probability for every point, and whether this might lead to issues in determining reasonable probability ranges (e.g. a 5% - 95% range of possibilities). In particular, the median point you reported in your latest summary, 262500, falls in the middle of a constant-slope segment of 100 bins (50k deaths).

(The results are not always constant over exactly some multiple of 10 bins; to be more precise, they looks like results I've gotten when trying to interpolate splines over a bunch of control points. There's sometimes a little bit of flex right around the knots or a slight change in slope partway between two points.)