We present new Hubble Space Telescope observations of three a priori known starlight-scattering circumstellar debris systems (CDSs) viewed at intermediate inclinations around nearby close-solar analog stars: HD 207129, HD 202628, and HD 202917. Each of these CDSs possesses ring-like components that are more massive analogs of our solar system's Edgeworth-Kuiper Belt. These systems were chosen for follow-up observations to provide imaging with higher fidelity and better sensitivity for the sparse sample of solar-analog CDSs that range over two decades in systemic ages, with HD 202628 and HD 207129 (both similar to 2.3 Gyr) currently the oldest CDSs imaged in visible or near-IR light. These deep (10-14 ks) observations, made with six-roll point-spread-function template visible-light coronagraphy. using the Space Telescope Imaging Spectrograph, were designed to better reveal their angularly large debris rings of diffuse/low surface brightness, and for all targets probe their exo-ring environments for starlight-scattering materials that present observational challenges for current ground-based facilities and instruments. Contemporaneously also observing with a narrower occulter position, these observations additionally probe the CDS endo-ring environments that are seen to be relatively devoid of scatterers. We discuss the morphological, geometrical, and photometric properties of these CDSs also in the context of other CDSs hosted by FGK stars that we have previously imaged as a homogeneously observed ensemble. From this combined sample we report a general decay in quiescent-disk F-disk/F-star optical brightness similar to t(-0.8), similar to what is seen at thermal IR wavelengths, and CDSs with a significant diversity in scattering phase asymmetries, and spatial distributions of their starlight-scattering grains.