Well, Phineas Fogg. You certainly picked a challenge!
Unfortunately, the 11/9/01 terror attacks had a severe effect on the permeability of our Canadian border. At least in the "Toward USA" direction, which was enough to kill the thru trains, buses and even walking across the bridge. The good news is it's not bad in your direction, and the US does not have exit controls. So you can just hitch a ride with high hopes of not being turned away at the border.
You might be able to hitchhike across the bridge, or find someone on social media making that crossing anyway who will give you a ride.
Don't cut the corner. Take Amtrak from Detroit to Buffalo.
It can be said, at least, that this is a sure thing. And paradoxically, it is the cheapest.
As you know, Michigan is a peninsula. As such, the major east-west trunk lines don't enter the peninsula, but that's OK - you're only an hour away from them at Toledo, Ohio.
So you book an Amtrak trip from Detroit to Buffalo. Cost is under $30 depending on date. Due to low ridership, the Detroit-Toledo segment is an express bus which leaves at 9:30 pm and gets into Toledo probably 10:45 pm give or take.
You are now on the route of the famous 20th Century Limited. Unfortunately your train will be its little brother The Lake Shore Limited. It comes through Toledo around - holy smoke! 3AM.
The ride gets you into Buffalo about 9AM. This is a full-service train with high attendant levels, and they should wake you.
American trains are subject to delay. Many people say bad things about that, but it's simply because these routes are breathtakingly long. The Lake Shore Limited is a "short" one and it's 1543km (Munich-Berlin x3). That means delays only accumulate (stack). This is just something you have to get used to.
Now to get from Amtrak Buffalo to Niagara falls, wouldn't you know it, there's an Amtrak train. But Amtrak's booking engine won't book it on the same ticket. A call to 1-800-USA-RAIL might get it on one ticket.