Any reason not to run directly off the 12v rail? It's a good quality seasonic psu with less than 1/3 of it's available wattage being used at max load and an overabundance of amperage.
After looking some more into this, others have mentioned that running a class t(d) amp (ta2020, tpa3116, etc.) will cause too much interference due to the fast switching nature of the amp. Given this, the tda7297 seems promising since it's a class a/b amp - not to mention that it's ridiculously cheap. The only thing I would be concerned about is that it only has a single 2200uf cap from the power supply. Will the single stock cap, or even an upgraded cap, be sufficient enough to smooth out the relatively dirty power? If not, is there any way to add more/bigger caps, etc. to clean it up?