Generate continuous random bit stream from noise

Several years ago, I needed a random bit stream for a microprocessor project. I built this circuit.

It runs off of 5 volts. The left hand side of the circuit is a charge pump to increase voltage to the transistor stages. They can be eliminated if you have a higher voltage available (about 20V IIRC). The 2N2222 transistor with unconnected collector operates in avalanche mode to generate white noise which is amplified by the other two transistors. It's then converted to a digital bit by the 74HC14, and goes to the microprocessor input.

In the program code, it uses Von Neumann's de-biassing technique to remove bias from the input bit stream:
Look at two successive bits. If they are both the same, then discard them. If they are different, use the first bit and discard the second. Warning: This algorithm can slow things down significantly if the input bit stream is highly biassed.

Edited to add:
Re-reading your original post, it appears that your main problem is a bias in the bits. Since you don't want to use an MCU, you could use your existing circuit, but implement the Von Neumann de-biassing in discrete logic. The problem is that this will affect the bit rate of your final bit stream. It won't be constant, and so you'll have to have some sort of buffer.

Another possible solution, if you can adjust the bit frequency bias by applying a DC bias somewhere in the circuit, you could provide a feedback signal to adjust that DC bias in order to cancel out the bit frequency bias. This is what I did in my circuit with the feedback components around the output Schmitt inverter gate.