This study focuses on high-energy proxies of stellar magnetic activity over long-term starspot cycles of three low-activity Sun-like stars:alpha Centauri A (HD 128620: G2 V),alpha Cen B (HD 128621: K1 V), and the Sun itself. Data sets include: daily solar ultraviolet irradiance spectra and X-ray fluxes from the Solar Radiation and Climate Experiment, during recent sunspot Cycles 23 and 24; Interface Region Imaging Spectrograph long-slit stigmatic imaging of solar Mgiih (2803 A) and k (2796 A) in quiet and active regions; and Hubble Space Telescope Imaging Spectrograph ultraviolet, and Chandra X-ray, campaigns on alpha Cen AB. Established stellar "flux-flux" relations, for example X-rays (T similar to 1 MK) versus Mgii(T similar to 8000 K), showed increasing power-law slopes with increasing formation temperature, but these give way on the Sun to bent power laws, and surprising inversions in the activity hierarchy: Siiiiis more "active" (steeper power laws) than Nv, despite the latter's four times higher formation temperature. The Sun's flux-flux behavior, nevertheless, remarkably parallels its low-activity solar twin alpha Cen A. In contrast, the cooler, somewhat more active, K dwarf companion displays correlations more in line with the previous stellar paradigm. The new flux-flux relations offer a way to vet numerical spectral simulations and proxy-based irradiance models, and extrapolate solar global activity indices into regimes below or above the grasp of contemporary records, or to exoplanet hosts at the low end of the Sun-like activity ladder.