Dual Engine failure you are on battery buses only, rat or windmilling for hydraulics.
The HDG is intended to extend the range beyond the 30 minute (design) limit of the battery powered standby system. Given a dual engine failure, I don't think anything beyond 30 minutes is really going to help.
Back when I was at Boeing, the question of 30 minutes came up. According to authoritative sources, it was an FAA requirement. Given a dual engine loss at maximum cruising altitude and optimal gliding conditions, I'm not certain if a 767 (or anything else) can remain airborne longer. But that issue was never addressed. There was (is?) a dual battery standby option required by some customers which may have been made to address this issue.
The HDG is intended to give a non time limited critical systems electrical supply in order to allow for diversion to alternate sites beyond the 30 minute battery capacity. This allows for operation further from such sites. Of course, this assumes you have at least one engine operating.
Starting the APU might assist in restarting engines or providing hydraulics (if windmilling is insufficient), but the battery standby system is adequate to support all electrical loads critical at this time.