Voltage Doubler Oddity

Just prior to tidying up and the workshop 'closing' for christmas, I've been playing with the CCFL transformers taken from a defunct LCD monitor, a simple blocking oscillator, and a Cockcroft voltage doubler.
As this transformer is rated for 3kV AC, I have been very conservative and used several 1N4007 1kV diodes, plus the 3kV 4n7 capacitors from the same board as the transformer.

I already knew from previous tests that when fed with 9V, the blocking oscillator, which is extremely simple, draws a lot of current, around 150mA, and the 2N3904 transistor gets hot, so had been working with 3V where it only took around 17mA.

To this simple blocking oscillator/flyback topography, I added the voltage doubler, and was disappointed to get only 550V from it. Thinking that I had no need for the spread voltage handling of three diodes per half-section of doubler, I changed the circuit to the more common form with just two diodes - and got under 400V!

Now, this has me confused! Why should I get a higher output voltage when I have more diodes, and hence more forward voltage drop, in series?

So, with this thought troubling me, I decided to try it on 9V. As expected, the transistor did get hot, though not as hot as previously. At a current draw of 37mA (interestingly having the ammeter in circuit lowered the output voltage as well) I was now reading a little above 1600V - 1800V without the ammeter.

Clearly this circuit is not at all efficient - in fact loading the mid-point of the doubler with a neon bulb and 4M7 resistor drops the output first to 40V, then slowly lower until there is no output, and the current drawn jumps to over 60mA! This can probably be improved by adding a feedback path to regulate the output. I have seen a Geiger circuit using this type of transformer, operating from 1.2V, admittedly supplying a standard 400V tube, and using a zener feedback system.

Update - The thought occurs to me that, with just the two diodes forming the Cockcroft circuit, the reason for seeing just 550V may have been due to the combined reverse breakdown of the two diodes! These are rated 1kV, but the pair operating across the AC supply from the transformer could well have been operating in a controlled breakdown on each half-cycle, resulting in the observed 550V. With three in series for each side of the doubler, the combined breakdown voltage of each chain of three would be 3kV - much more than the applied voltages, and hence the more sensible 1500V output.