Avalanche diode random source design
I'd do it like this (assuming that you had a comparator available somewhere, perhaps in a micro controller.  You might need a couple of AC coupling capacitors to control the DC bias):-



I don't like building boosters as it's unreliable judging by the number of such questions on this forum.  If you want the lowest risk approach to more volts, I buy in and use a commercial DC-DC converter.  You can get a +/-15V one for £10.  I know that these work and are the most effective way to make 30V.

This gives you lots of volts which means that you can dump the transistors and go for a proper avalanche diode.  You shouldn't really be using transistors as they aren't stable long term and you'll have trouble calculating next year's entropy output due to degradation.  A transistor is not designed to run backwards.  A 24V Zener will fit the bill nicely and create > 1V peak-peak noise over 12,000 samples as shown below:-



Ignore booster noise.  It will be totally overwhelmed by the avalanche noise.  And don't bother with Dieharder - you'll never generate enough data to use it properly.  Just categorise the entropy with the original Diehard, ent or simple compression via 7z (I use fp8 which is much better).  The beauty of compression entropy estimation is that the sample data can be ASCII, binary or Klingon irrespectively.

Ignore bias /correlation in the entropy stream.  The solution is to just collect 100x the entropy you're looking for before whitening with something like SHA-1.