The Manitouwadge route is definitely the shortest. It's probably 90 minutes quicker than taking Hwy 17 all the way to Nipigon and then backtracking north on Hwy 11. There is a gas station in Manitouwadge, but I don't believe it's open all night. However, the Nipigon route is definitely going to have several 24 hr gas stations along 17. You may also consider filing up some jerry cans with gas to get you through.
Either way, you may want to reconsider your timing. I have driven across northern Ontario hundreds of times over the last 50 years, and I almost always avoid driving at night. I've just seen too many collisions with Moose, to know that's its not an uncommon occurrence. Be very, very vigilant. I would leave earlier, spend the night in Nakina and be bright and fresh for your fly-in that morning.