Really, Lake Ontario makes any NY-Detroit train line much longer than it could be otherwise.
VIA Rail advertises that its Toronto to Windsor service is a great alternative to driving and flying. It is 1 hour slower than flight and about equal to driving. Surely they can make some good improvements. EDIT - I just discovered that Ontario has committed to bring the Toronto to Windsor line to 200 km/h by 2025 and 300 km/h by 2031.
A brand-new bridge between Windsor and Detroit has already been approved. Canada is paying for 100% of it, why not add rail capabilities (like the Øresund bridge between Sweden and Denmark)?
The Detroit to Chicago Amtrak line runs at > 100 mph for almost the entire length already (paid for by the "car-friendly" state of Michigan). The major bottlenecks are two counties in Indiana that Pence hates. With him in Washington, he might still find a way to block construction, but then again he might be too busy to get involved in such piddly things anymore.
So basically, you just need to find a good way to speed up the current New York to Toronto Amtrak, which is 12.5 hours to go 350 miles!
Reaching the absolute minimum NY-Chicago travel time isn't necessarily the highest priority because at that distance you're not going to beat a plane and you're probably not going to see same day round trips. Instead making the line economical by including as many people as possible would make the trip cheaper for people who can't afford flying. You could even add stops in Philadelphia and Toledo, which aren't too far off course.