I'll answer my own question since I found a way to do almost exactly what I needed (with some improvements!), and I'll describe it here for posterity.
I found the "Segmentation Editor" plugin:
http://132.187.25.13/home/?category=Download&page=SegmentationEditorwhich allows for me to do what I needed almost as I described. With this plugin, you can manually set ROIs in several slices (even more than one ROI per slice) using the ImageJ selection tools (you can skip some slices and then interpolate the ROIs in between) and use some additional functionalities (opening, closing). When done, this plugin creates a 3D mask image. You can save this image or then use Analyze->Tools->Save XY Coordinates if you need a listing of the x,y,z coordinates in text form. Very useful.
Hope this helps anybody else looking for similar functionality.