Thank you everyone for all the info and ideas, and schematics! I should have enough here to make something work, I'll post back with my final solution.
Thanks for the suggestion. I did check this out right when you posted it, and if I understand the data sheet correctly the turn-off timer actually sets the duration of the long-press required to power off, as opposed to the duration before it automatically powers off after turning on.Was the the LTC2955 device not appropriate or too expensive?