Bring a tent, a warm sleeping bag, and camp for the night? (Too bad it isn't summer) for the layovers.
I think the easiest thing to do would be just a round-trip to and from Sault Ste. Marie. That would unfortunately involve some rides on Indian Trailway Routes all subsidized by the state of Michigan. (Looking this information up was sort of research related, I'm in the process of writing a grad school paper evaluating intercity transportation options to rural Areas, Amtrak will definitely be in there so there is some benefit for me, if you do take these bus trips I would deeply appreciate a report, particularly on crowding and usage).
I was just playing around with Bus schedules on the Indian Trails Website and the two different Amtrak's Indian Trails Thruway connections to St. Ignace that follow different routes but arrive at 11:40pm and 11:50pm respectively have direct connections to buses to Sault St. Marie, Michigan:
The Bus leaves Ignace at 12:15am and arrives in Sault Saint Marie, Michigan at 1:08am. For some reason Amtrak doesn't offer a thruway connecting to another bus to these buses.
You can also connect to Sault Saint Marie via the Wisconsin side and across the Upper Peninsula, changing buses in Escanaba, Michigan from the Amtrak Thurway connection there from Milwaukee. It's dead overnight, leaving Milwaukee 9:45pm Arriving Sault Saint Marie 7:45am (too close for comfort for me at least to get across the border and catch the 9:00am Railway train).
To get across the border take the
bridge bus it runs every hour. If you caught the 7:00am bus (first one from the Michigan side) I think you'd make the 9:00am train departure, trip is about 20 minutes over the bridge. The last bus from Canada leaves I think at 6:30 weekdays, 4:30 weekends. You could make that connection going south to (if the trains on time).
Wish there were better options!
Return is similar: The via Lower Michigan (I think that's the right term) bus leaves at 7:40am to connect in St. Ignace, via the UP and Wisconsin via Escanaba is at 1:13am.
I think this would be a great trip, If only the Ontario Northlander still ran you could very easly connect to that train going the other direction from Hearst, there is a connecting Ontario Northland Bus leaves Hearst once a day at 5:00am and connects to the Ontario Northlander Polar Expess:
Ontario Northlander Bus:
Dp. Hearst - 5:00am
Ar.
COCHRANE - 7:45am
Polar Express train: Lv. 9:00am do a same-day round trip getting back to Cocharne at 9:42pm (it runs Monday through Friday)
Connections at 11:45pm back to Hearst. (guess you'd be stuck spending a full day in Hearst before the next Algawa Canyon train back)
Day bus to Toronto Dp. 8:30am Ar. 9:15pm (You can connect from the Polar Express to a bus to Timmons directly Ar. Timmons 11:30pm, Bus Dp. 11:30am Ar. Toronto 9:45pm) – strangely no overnight Northlander buses. The 5:00am bus from Hearst spends all day on the road and can eventually get you to Toronto (9:15 to 9:45pm)