The MeasureObjectAreaShape module in CellProfiler provides the basic morphological values for an identified object, such as perimeter, etc. However, CellProfiler doesn’t currently provide the measurements you mention as an explicit output. So, no, you weren’t overlooking anything
However, if you used IdentifyPrimAutomatic (or a similar module) to pick out the cells, you might consider using ConvertToImage to convert the cell objects to a label matrix and then saving the label matrix to a file with SaveImages. A label matrix labels connected components (such as cells) in an image and might be further processed to get the additional parameters you need. If you are fluent in MATLAB , I suggest attempting to manually extract the parameters you want from the label matrix.
Hope this helps!