Thanks!
I forgot to mention that I figured out how to do multiple galleries per post (with different images, as you choose).
You just need to give each image a media tag, and give each set a different one (like gal1, gal2, gal3, etc), and then click the ‘switch to tags’ button in the editor, select the tag you want (like gal1) and then it inserts all images tagged as that gallery.
Here it is in action for those curious.