Rewrite to use new data structure and update most of task

Use a single data structure to hold both the intermediate data and the final
results in a sensible format.

Change how the exclusion of data points is handled to make it understandable
and persistable, especially so that other tasks can use the outputs.

Improve robustness of fitting for curves that fully turn over.

Correctly seed the initial parameters for fits and add limits for fit params.

Fix bugs in the output messages and their formatting.

Fix several logic errors.

Fix typo meaning that errors were incorrectly reported in plots.

Update tests for new code structure.

Remove dangerous use of default value in function arg

Update weird/bad values used in tests