The author of the HRNG link you posted claims to have gone to some effort to reach his goal, namely
trying to design a circuit that could produce a symmetrical, zero-average noise signal from a reverse biased p-n junction in avalanche breakdown
but it really isn't clear how he achieved and verified the output of the hardware other than with software. Your circuit has no provision for adjustments and can't produce a zero mean signal. Also, he used a digital input to generate "1"s and "0"s -- your use of the ADC throws in an additional complication. So you may be fighting an uphill battle.
I don't mean to be discouraging! These things are fun and challenging.
As an aside, it is interesting to listen to various different transistors in avalanche breakdown. You can do this by coupling the output transistor via a capacitor to the high gain phono input of an audio amplifier. There are a few different processes that lead to breakdown, and these manifest themselves as clicks, pops and hisses of different apparent pitches.