..Ook champ, so I can't restore that..
Other than the serial, Incognito changes a bunch of things:
erase(0x0AE0, 0x800); // client cert
erase(0x3AE0, 0x130); // private key
erase(0x35E1, 0x006); // deviceId
erase(0x36E1, 0x006); // deviceId
erase(0x02B0, 0x180); // device cert
erase(0x3D70, 0x240); // device cert
erase(0x3FC0, 0x240); // device key
At least some of these (likely all of them) are required for online functionality, and they aren't stored anywhere else in the system AFAIK. That's kind of the point of Incognito, if it didn't erase everything used for online identification it wouldn't be doing its job.
In theory it is possible to use certs etc. from another console to spoof that console to go online, but there's no way to make that work on current CFW.