Radio spectrum is a scarce resource. To meet demands, new wireless technologies must operate in shared spectrum over unlicensed bands (coexist). We consider coexistence of Long-Term Evolution (LTE) License-Assisted Access (LAA) with incumbent Wi-Fi systems. Our scenario consists of multiple LAA and Wi-Fi links sharing an unlicensed band; we aim to simultaneously optimize performance of both coexistence systems. To do this, we present a technique to continuously estimate the Pareto frontier of parameter sets (traces) which approximately maximize all convex combinations of network throughputs over network parameters. We use a dimensionality reduction approach known as active subspaces to determine that this near-optimal parameter set is primarily composed of two physically relevant parameters. A choice of two-dimensional subspace enables visualizations augmenting explainability and the reduced-dimension convex problem results in approximations which dominate random grid search.