Ultrafine ("nano"-) particles produced from highly supersaturated vapors or liquids often undergo rapid coagulation and slow interspherule coalescence. Resulting "aggregates" typically contain hundreds of small spherules bound together in tenuous structures characterized by mass fractal dimensions much less than 3. Such aggregates have large and relatively accessible initial surface area but are metastable with respect to more compact configurations, especially in high temperature environments (e.g., flames). Subject to deliberately idealized "uncoupled" rate laws for coagulation and coalescence, we illustrate the power of Monte Carlo simulation methods to obtain the self-preserving joint distribution function (with respect to both particle size and surface area) of populations of coagulating fractal aggregates in the continuum regime, simultaneously undergoing finite-rate restructuring (e.g., via surface-energy-driven viscous flow). Unconditional distributions with respect to either particle volume or area are also obtained from the Monte Carlo simulations. These are conveniently quantified by fitting them to log-normal distributions and we report the sensitivity of the associated spreads to characteristic fusion/coagulation time ratio, chi, and particle fractal dimension, D-f, here prespecified. We also calculate and report selected "mixed" moments of the joint pdf with respect to particle volume and surface area needed for engineering calculations of deposition or diffusion-controlled vapor scavenging, as well as the important ratio of actual mean area to that area corresponding to the mean particle volume in the aerosol population. This work sets the stage for tractable simulations of particle dynamics in more complex coagulating systems requiring multi-internal (state-) variables for their more realistic and self-consistent description.