It's really tragic and inelegant how we have to jump through hoops and bounce files around a wireless network when the USB cable is just sitting right there. What I had to do since rsync doesn't work with mtp file paths was to install android-file-transfer and run the following with my phone connected via USB, but not already mounted by the file manager:

aft-mtp-mount /path/to/mount/point
rsync -a --progress --exclude 'Android/' '/path/to/mount/point/Internal shared storage/' '/path/to/backup/'

You can also omit the --exclude 'Android/' part as needed, I just didn't want to copy over the quintillion tiny files under that directory.