Bias is a good guess. The Zombie uses a single bias voltage to serve as both bias voltage for the BBD and Vref. As has been discussed here on many an occasion, that's an elegant compromise, and it certainly pares down the parts count, but it doesn't always work well.
There are a few ways you can tackle it. If you look at the schematic for the CE-2, you will see that Boss does what Hollis does, and that is to insert the bias voltage earlier in the audio path, and make sure there are no DC-blocking caps between that point and the input to the BBD. Boss inserts the bias voltage or the BBD at the input to the filter just ahead of the BBD, so that the signal rides on the bias voltage through the lowpass filter and arrives at the BBD input on top of that voltage.
At the same time, Boss uses a separate V+/2 bias voltage for the LFO, where Hollis uses just the one bias for every part of the circuit.
If you look at the Small Clone schematic (try the Heladito at Tonepad), you'll see that a standard V+/2 bias voltage is used throughout the circuit except for the BBD, but here too the bias is inserted just at the input to the lowpass filter before the BBD.
Looking over a variety of schematics, the smart thing to do is probably to set the Vref resistors at 10k/10k for the existing board (instead of a non-midpoint Vref using 10k+15k), and supply a separate bias voltage to the BBD at its input (pin 3) on some kind of little daughter-board. Use a 10k trimpot, with a 2.2uf-10uf cap from wiper to ground, and a 22k-100k resistor from wiper to BBD input pin. The noncap end of the trimpot goes to V+, and the other to ground. The wiper feeds the BBD a bias voltage between 9v and 0v.
Since there already is a bias voltage fed to the input of IC1a, you probably want to "reset" things by sticking in a DC-blocking cap between the output of IC1a (pin 1) and the input of the BBD (pin 3). This will let the existing Vref come along for the ride with the dry audio signal to the mixing point, but cut it out for the BBD, which will have its own bias voltage.
That should let you dial in whatever a suitable bias voltage is for that BBD chip, without producing problems elsewhere in the circuit.