The Franken-firmware is 11.6 (maybe higher now, it's been a bit) but it has 6 titles downgraded to 11.2 so GW works.
Thanks for the detailed response. Can you give me any more pointers to finding out about making a franken-firmware? I'd like to get this working so that I can play any .3DS just by putting it on a MicroSD card. I did find 3DS Multi-EmuNAND Creator which ought to be useful for this.
...I'd like to save a load of time avoiding bad CIAs
It turns out the SD card where I'd copied my .3DS files from had gone bad and the files were duds. Urgh. Although that doesn't explain why I haven't been able to make working VC CIAs.