I maintain that you can get slightly more than 14 bit with Paula (with real Paula ; not in emulators which are really limited to 14 bit).
Remember that we use two 8-bit DAC for playing single 16-bit sample. If we could shift the volume 8 positions we would get full 16 bit. But we can only shift 6 bits (volume 64 vs volume 1). So in theory this is 14 bit, but the output is nonlinear so we have more combinations than just 16384 ; by reordering them cleverly we get over 14bit accuracy.
A good 14-bit routine plays 16-bit samples, not 14-bit samples.
Sure i'm not electronics engineer but i've seen the code and you have not.