Cannot get the interpolated profile Horne extraction to produce the correct normalization for the extracted spectrum

The extracted spectrum has negative normalization (kind of mirroring the gaussian Horne or boxcar extractions). I tried various combinations of parameters, but cannot figure out where it is getting a negative normalization.

Here is the data: "mast:HLSP/jades/dr3/goods-n/spectra/clear-prism/goods-n-mediumhst/hlsp_jades_jwst_nirspec_goods-n-mediumhst-00000804_clear-prism_v1.0_s2d.fits"

Here is a plot of the extraction:

Start by reproducing the interpolated profile Horne extraction with the supplied MAST FITS dataset and the parameter combinations described in the issue. Trace how the extraction computes normalization and compare it with the gaussian and boxcar results. Done means the extracted spectrum no longer has a negative or mirrored normalization and the corrected behavior is covered by a regression test.

Written by the indexing model from the issue text.