DC biasing arrangement in this audio phase shifter circuit
Your post, rather unusually, hasn't attracted any answers.


  Part of the circuit I do not understand is the DC biasing arrangement. I can see that it uses a 4.5V Zener diode to provide the 1/2 VCC supply as this circuit runs off single 9VDC supply. 


Correct.


  I do not understand how the 4.5VDC gets to the stages. Do R6/R9/R12/R15 provide the DC component to the stages? Or does R2/R3 simply bring the DC to the first stage and it gets passed through each stage?


Let's have a look at the first stage, OP1. This is a non-inverting stage with a gain of \$ 1 + \frac {R4}{R3} = 1.2 \$ approx. The non-inverting input is fed from a high-pass filter with a -3 dB of 14 Hz. Note that there is a DC path to the 4.5 V rail for the bias currents from both inputs. This prevents problems with offsets on the outputs.

The result of all this is that OP1's output will be centred around 4.5 V and this "bias" will be fed into the subsequent stages.


  Finally, I can't figure out the purpose of R18, the 1k resistor at the output of the last stage.


I suspect that the answer is as follows:


The phase-shift stages act as a difference amplifier between the direct and phase-shifted signals on their inverting and non-inverting inputs respectively. The output of each stage is somewhat attenuated.
For a good phasing sound the phase shifted signal requires some amplification before being mixed with the resistor mixer consisting of R20, 21 and 22.
By taking the feedback point from the junction of R17 and 18 a gain of 3.2 is applied to the OP5 stage. (Don't forget that we already had a gain of 1.2 at OP1 so the overall gain is \$ 3.2 \times 1.2 = 3.84 \$ or almost 4.
It seems to me (and you, I suspect) that the same effect could be obtained by omitting R17 and 18, changing R16 to 320k and connecting it to OP5 output. Someone else may see a rationale for this but, like you, I cannot.




Debugging via comments:


  ... all opamp stages have about 4.5VDC except OP5 which has only 2VDC. I get good phasing sound from all output stages except OP5. The input pins of OP5 have good phasing sound and signal amplitude, output is attenuated.
  
  R18 is correctly connected to 4.5V rail. One side of R18 measures 4.5V the other side measures 3V. 
  
  I've also swapped last output opamp with another known good and problem persists. 
  
  To clarify OP1+OP5 make up one dual opamp, OP2+OP4 make up another, and OP3+OP6 (OP6 being the LFO generator) make up the third. – disorder 6 hours ago
  
  Voltages at outputs as follows. OP1: 3.35V, OP2: 5.08V, OP3: 3.27V, OP4: 5.09V, and OP5: 1.94V.


I was expecting about 4.5 V on each. It seems to me that OP1 might be the problem as its output is 1.15 V low. Each stage is inverting for DC signals so you're seeing the DC error alternate. OP1 is low, OP2 is high, 3 - low, 4 - high and OP5 with it's gain of three is very low. 

The 1458 datasheet says on the bottom of page 2 that the output swing into a 2k load is only +/-13 V when powered from +/-15 V. That means that it can, at best, swing to about 2 V above negative supply. Since you're on only +9 V the situation may even be a little worse and your opamp output is now presses as low as it can go.

Go back to OP1. There's something wrong there. Ideas:


Get a precise voltage on the 4.5 V rail. I suspect it's lower than that because of the alternating op-amp output voltages - maybe 4.2 V. That itself isn't a problem.
Check the voltage on OP1 + input. It should be the same as the "4.5 V" rail. If not we're getting DC from somewhere. 


Check that R2 is connected to 4.5 V and not GND.
Check that C1 isn't leaking and pulling that input low. (Disconnect one lead of it or measure voltage across R1 - it should be zero if no DC is flowing.)

If you draw a blank on that then try adding a resistor from OP1 '-' input to ground. This will make the setup into an inverting summing amplifier. Start off with about 1M. The effect of this should be to bias the output upwards by \$ V \frac {Rf}{Ri} = 4.5 \frac {100k}{1M} = .45 \; V \$. Decrease the R value to move it more positive. The idea here is to get the DC back on centre. It doesn't explain the problem but would get the setup working enough to prove that everything else is OK. If so then go back to OP1 and figure out what's up.