I just double-checked the RSF file, and it seems I disabled one too many services: the ac:u service. The ac:u service is used for checking the Wi-Fi status. This doesn't explain why it still worked on my system, though...
Test build:
http://gerbilsoft.soniccenter.org/T...-22.bugfix.fix-sounds-on-updater.63f672db.zip
I verified with someone else who was having the updating issues and this build fixed it for them. No idea why it worked on my 3DS without this...
EDIT: Found it. Luma3DS's "Enable game patching" option seems to disable service access checks. Turning it off prevented boxart downloading from working on 3.0.1, but it works on my new build. (As a workaround, you can enable the option to get updating working on 3.0.1.)