So, what to do? After much Googling, I found the answer in another app that I already have and use on my phone. ES File Explorer, which I found is handy when I want to move stuff around while I'm at home, on my WiFi network.
Open Es File Explorer, and press the press the globe/phone icon in the top left corner. You should see this menu:
Click on the Cloud option, and then link it with your Google Drive account. Now when you open up Drive from here, you can select the files you want by long-pressing (push and hold on the file until it becomes selected with a check mark in the corner) and selecting the "More" option from the bottom bar, and choosing "Move to" from that menu. From there you can save the file wherever you like. I chose to put my picture in the "Pictures" folder, where it then shows up in my gallery.
Hopefully, Google with add a way to do this on their own straight from the Drive app, but until then, this way get the job done.