Because the galaxies of the Local Group have such large angular sizes, much of their diffuse, large-angular-scale emission is filtered out by the Herschel data reduction process. In this work, we restore this previously missed dust in Herschel observations of the Large Magellanic Cloud, Small Magellanic Cloud, M31, and M33. We do this by combining Herschel data (including new reductions for the Magellanic Clouds), in Fourier space, with lower-resolution data from all-sky surveys (Planck, IRAS, and COBE) that did not miss the extended emission. For each galaxy, we provide this new Herschel data for 5 Hershcel bands: the PACS 100 and 160 micrometer bands, and the SPIRE 250, 350, and 500 micrometer bands. This data is provided in FITS format, with one FITS file for each band for each galaxy. Each of these files contains 4 extensions. Extension 1 (IMAGE) provides the standard feathered map. Extension 2 (UNC) provides the uncertainty map. Extension 3 (MASK) provides a binary mask map indicating the portion of the data where reliable, fully-feathered high-resolution coverage is available. Extension 4 provides the foreground-subtracted version of the feathered map (FGND_SUB), the header of which also describes the uncertainty on that subtraction. Original acknowledgement for data: C.J.R.C. and J.R.-D. acknowledge financial support from the National Aeronautics and Space Administration (NASA) Astrophysics Data Analysis Program (ADAP) grant 80NSSC18K0944.