A backup battery or PMA (dedicated "permanent magnet alternator" sure is the best solution, though probably heavier.
Even if the procedure to start the second engine on ship power only is followed, this would probably not prevent a FADEC shutdown during gear operation in other cases (e.g. single engine go-around with a weak battery or high current draw on the gear motor due to a mechanical gear fault -
AFAIK this has resulted in complete loss of electrical power on other light A/C in the past.)
I would have supposed that there is some way to extend the gear without juice to avoid the "neither up nor down" scenario you described.