yeah, i also think that is related to battery. i disassembled my tab few times, tried some combinations with on/off internal switch, no luck with apx. also tried to ground 'charging' socket - all one by one pins of it. without result. also tried special service microusb cable, with 3 options with resistors - which i use for example for galaxy s - to force download mode - without luck on sony..
about grounding - testpoint - a lot of sony ericsson phones had backdoor in that way, simple grounding one point of service interface.
today i thought about nfx services - they're involved in all of that recovery mistery, decrypting update.zip, and i think that also in apx thing.
apx mode appeared when i was trying to get root - again after hmmm... 5-10 failed try. so maybe nfx logged some number of reboots, reboots in random time, when copying, when some adb commands where running, and forced device to apx mode?
of course its just a theory