How can I quickly publish all subalbums and all images within a chosen album(s) ?

You could use the included publishContent plugin.

I can see the "Propagate un-published state" button, but... what I actually need is "Propagate published state" and there is no such option... :-(

I work this way: I import images (default: unpublished), create albums (default: unpublished), I sort them, describe, review, etc... When it's ready - I want to publish the whole album tree.

You can fold out the subalbum and images list and then select what you wish to publish.