I'm unable to recharge any of my two A780 batteries, at least not via USB. Since I'm travelling, I cannot try with the real power-supply charger. Let's hope I can somehow resolve this, and it isn't really some damage to the phone's built-in charging controller :(
On the A780 hacking front, I've now successfully confirmed that there are indeed JTAG pads on the PCB, both for the PXA270 and for the ARM7TDMI, which is great news.
I also think there is still hope that the USB device port could actually be used as a host port. At least the PXA270 supports various options for OTG. Now the big question is only whether this is compatible with Motorola's overloading of the USB (called Enhanced Mini USB).