Restoring a pre-A9LH FW SysNAND dump to SysNAND should not brick your system (just avoid restoring an EmuNAND dump to SysNAND, that tends to brick systems). However, you might want to try it with the "keep a9lh" option, since that will allow you to keep A9LH, and see if that works first. Keeping A9LH should not prevent a good TWLN partition from functioning, after all. But if it doesn't work, you can try restoring it normally. You can mount the sysNAND_original.bin with GodMode9 to extract the TWLN.bin through the virtual file system. After mounting, it takes you back to the root, then you go to "IMGNAND VIRTUAL" and copy the twln.bin to the SD card (for good measure, you might do twlp.bin as well, though that really shouldn't have anything to do with primary DS functionality, since all it does is store photos). You could also restore "sysNAND_original.bin" using the "keep A9LH" option in Decrypt9, then extract the TWLN partition using Decrypt9 (only if you can bring up DS wifi settings after the restore though, otherwise, there's no point). It almost has to be a messed up TWLN partition if you can't even get the DS wifi settings to show up. I would think there would be at least one good backup, though. Especially with the A9LH installation procedure having you make so many of them.
Your problem is definitely unusual. I've not had any problems with DSiWare, or even my old Acekard 2i, on any of my systems. And I'm just running the regular stable release. I do have an "AIO A9LH Configurations" package on the iso site if you want to try other CFWs just to be sure it's not an issue with Luma. It seems extremely unlikely, but you might as well rule it out. Also, Corbenik and Cakes do load external copies of the TWL firmware, so they might get some things working, even if using them probably won't actually solve the underlying problem. I guess it's possible that the TWL part of the NAND has just failed (I would expect there to be an error when restoring the TWLN partition if that was the case, though). I'm not sure what to tell you. I've messed up my TWLN partition before, and the result is exactly what you describe. However, restoring a NAND backup has always fixed it for me.