Would NFB really add a significant change in sound quality?
Solid state amplifiers have extremely low distortion at any power level becaue their open-loop gain is high and a lot of negative feedback reduces the gain to a useable amount and also reduces the distortion. The negative feedback makes the output have an extremely low impedance (0.04 ohms or less) for good damping of the resonances of a speaker.
I'm using a transformer for the phase splitter now, if I drove that by a transistor, could I add NFB?
A transformer causes phase shifts so only a small amount of negative feedback can be used to avoid oscillation. Your amplifier does not have much gain.
It is a class-A heater with low output power. Each Mosfet heats with 25.5W all the time!
The highest output power on the distortion graphs is only 4.2W.
The output transformer is huge, heavy and very expensive.