You can't inject FBI into the N3DS H&S app. I tried that. It said that the H&S app was missing the TMD.
I'll see if I can try it in Ninjhax 1.1; see if that makes any difference. It shouldn't.
You can, actually. My EmuNAND has the regular Health & Safety app replaced with FBI. I also followed Sgt. Lulz' tutorial on how to set up CFW, which actually said this was the only method for New 3DS users.
Granted, that was a while ago when the tutorial still recommended rxTools (it's been updated to use CakesCFW instead), but it should work fine if I recall correctly. I did have issues injecting it into my SysNAND's Health & Safety (it later turned itself back to H&S I think), but it might be because I missed a step somewhere.