So, he made some more shelves recently (and I helped stain the boards). Thursday, we finished putting the movies and TV shows in the new shelves, and yesterday I shifted our collection of anime DVDs down a few shelves so it now has room to expand. I also went through the console games and organized them (because the new shelves meant we didn't have DVDs on the rack where the console games are anymore).
I'm very pleased with the results - we no longer have a pile of videogames reaching part-way to the ceiling (because there was no place else to put them), and we have room for the DVDs we got for Xmas. This will also make it much easier to find things.
Yay for more storage space!