Quiet Diodes at Audio Frequencies
Diodes, pretty much by definition, are non-linear components, which means that they always distort your signal. The trick is to operate them within a range small enough to make the nonlinearity so small that you cannot measure it.

The point of why people use diodes in biasing is that if you pick a saturated operating point, the voltage across the  diode will not depend much on the current passing through it. That's pretty much the opposite of what you want – you'd fix the gate at \$V_{cat} + V_F\$, and that's it. All signal that you apply should basically be "swallowed" by the diode.

The diode types you mention are old to positively ancient. The 400x series are rectifier diodes, ie. optimized to be nonlinear. The 914 is the predecessor of the already practically obsolete 1N4148 series – seriously, where would one even dig up such old components?

Old diode types are not preferable if you want low noise operation.