Though I'm now in Canada, which means I don't have access to much test equipment, Mike is extremely supportive, and has hired an engineer, in Shenzhen, to investigate on our behalf.
I did borrow an old, analog multi-meter from a friend, and actually it turned out to provide better readings than my digital one back in Taiwan! Where previously I was getting spurious readings - resistors that I knew are 50 kΩ were reading 40 kΩ or 10 kΩ or 70 kΩ depending on surrounding components: the analog meter said, categorically, "1 kΩ" when connected to a 1 kΩ resistor. Now, it may have been a fluke, however I swear that for about one second the voltage from the SY8008B actually read 3.3 V, just as it was supposed to.
I thought about this for a while, and there is another quite simple hypothesis: the BGA balls on either the A20 or the DRAM - more likely the A20 - are shorted out. The AXP209 PMIC is detecting this, and shutting down the SY8008B. The only way to check this is with an X-ray of the assembled PCBs, so that's what Mike is arranging. He'll send me the images for inspection, the moment they're available, and you'll be able to see them in a future update.
A couple of years ago, I spent some time with an extremely knowledgeable PCB designer in Taiwan. He told me something that could be very relevant, here, about PCBs with fine-pitch BGA. PCBs are etched with acid, and when the tracks or pads are particularly close together (such as with BGA balls), not enough acid gets in to eat away the copper, and (in a very indirect way) the BGA pads end up being far larger than they should be. This, in turn, means that when the IC is put on the PCB and heated up, the BGA balls (which are made of solder) will spread out much farther, and potentially even spread so far that they contact each other and short out.
With the production PCBs being done in a different fashion from the prototyping ones, there is the outside possibility that the BGA pads have turned out "oversized." It's just one of those weird things of PCB manufacturing.
Again: apologies to people who keep asking "when will I receive my shipment?" - the answer has to be, "when all the unknown and unknowable issues have been investigated and eliminated, one at a time."
This is just how it is.
Normally, a mass-volume product, made by a proprietary business, would never, under any circumstances, announce the product until it was absolutely and definitely final and already in the mass-volume production pipeline, almost on the shelves. Their "reputation" would be "destroyed," their customers would panic if the slightest word got out of "problems," and so absolute total secrecy is the utmost priority.
Crowdfunding, on the other hand, is radically different: you back the idea, and the story and the journey is what you get to see, no matter what happens: in fact telling people exactly what happens is extremely important!
I'm grateful to those people who get it and say "thank you" for the level of detail and the description of the experiences that we've had, because for their project, they then know what to expect, and enjoy being educated on the kinds of pitfalls that might occur, and how to get out of them. I learned from the OpenPandora and the OpenMoko and many other projects, and am repaying that in kind.