Not sure where in Michigan you are, but I just did Google Maps from Traverse City to North Sydney and it said 25 hours. Maybe that still too far to drive for you, but I think worth considering with the high moose population in NF.

You didn't say what type of moose you would be happy with (cow, any bull, certain size bull)?

Personally, I would stay away from Quebec. Their track record with outfitters and caribou hunters is terrible. Just my 2 cents.