Observations with the Karl G. Jansky Very Large Array at 46 GHz (7 mm) have been used to measure the size and shape of the radio photospheres of four long-period variable stars: R Leonis (R Leo), IRC+10216 (CW Leo), chi Cygni (chi Cyg), and W Hydrae (W Hya). The shapes of the stars range from nearly round to ellipticities of ~0.15. Comparisons with observations taken several years earlier show that the photospheric parameters (mean diameter, shape, and/or flux density) of each of the stars have changed over time. Evidence for brightness asymmetries and non-uniformities across the radio surfaces are also seen in the visibility domain and in images obtained using a sparse modeling image reconstruction technique. These trends may be explained as manifestations of large-scale irregular convective flows on the stellar surface, although effects from non-radial pulsations cannot be excluded. Our data also allow a new evaluation of the proper motion of IRC+10216. Our measurement is in agreement with previous values obtained from radio wavelength measurements, and we find no evidence of statistically significant astrometric perturbations from a binary companion.