I have found my lg vs700 (verizon) rebooting by itself, also, however, no "damage" is done as with yours - changing things. I suspect my issue is a "normal" badly programmed phone - because it has other issues, too.
Yours suggests a broken phone, possibly battery (or connection) problem or bad charger problem. I say these because rapidly flicking power can make hardware do strange things, also, I once bought an extra charger from ebay and it would take over my old motorola droid phone - cursor jumping around, executing random things - I'm guessing that the charger had a lousy hum filter and the power was not clean. I can use this to charge headphones, etc, but not phones.
If it is not too late, I'd ask for a replacement - if it is a bad board problem, you'll never fix that. (I'd also take out the battery, wipe the contacts, look for gunk where they contact and also check if the problem only occurs on the charger.) Good luck!