Supplementary data for arXiv:2606.01966v1 The supplementary data comprises of: - Exclusion limits for the "BP3" benchmark points, including comparisons to ATLAS, in csv format, for the resonant, non-resonant and heavy-resonant (20% width) models. - Exclusion limits for the 140 new, "optimised" benchmark points from Karkout et al 2024, which we have called the "ODRB" points, in csv format, for both Run 2 (ATLAS) and the HL-LHC (3000 invfb). These two csv's extend those given by Karkout et al. - Auxiliary Figures: plots of NN inputs and outputs for two additional points not included in the main body of the text. - 15 YODA files for the validation of the NN inputs and outputs at five parameter points, for Rivet and CMS, alongside the ATLAS reference (the reference was not provided by ATLAS on hepdata, we extracted the values as best-possible from the figures in the aux material). - Alternate versions of Figures 6a, 6b and 7, which include a comparison to the ATLAS results recalculated without the inclusion of those signal systematics which could not be applied in the Rivet and CheckMATE procedures. Named *_noSigSyst.pdf. - Example MadGraph cards for the (317.7, 594.0) point at 13 TeV in a tarred directory - A tarred directory containing example scripts (and necesarry associated material) for going from a Rivet YODA file to a likelihood using HS3.