The potential issue here is matching the two precisely enough. When you are working with 10bit that last bit is worth 0,1%. So the ration between the two amplifiers has to be within that, otherwise the smallest bits end up turned into just extra noise.
The actual solution is better methods of modulation. There is no strict rule to use PWM, anything that switches well out of the audio range will work. A single pulse does not need the full output bit depth since what counts is the sum of everything within the sample time. Things like sigma delta use this to distribute the error out by keeping track of the error and driving it towards 0. Most of the modern audio DACs you end up listening to are actually just 1 to 5 bits running at 1 to 50 MSPS, it's the sigma delta modulation placed in front of them that makes them capable of playing 24bit audio with noise figures in excess of -100dB