A Gainclone chip amp makes for a nice benchmark/monitor amp. How can I add controllable even order harmonic distortion to one?
The simple answer is that you can't. The reason these are so cheap and simple is that there aren't a lot of configurable parts and sadly you are stuck with odd harmonics if you overdrive the LM 3886.
As JimR said, you'll need to use a valve overdrive in your signal path if you do want that sound.