Not being a native of Michigan City or even the midwest, my opinions should be treated with a grain of salt, but I have one concern with this plan. That is, that the phrase "Eminent Domain" is a four-letter word these days. That alone may, in the end, make the North or the South route the only practical one.
Fear, distrust, and dislike of "eminent domain" is to some degree seeded deeply in the American psyche. I theorize that it stems from a basic, overriding mistrust of government that you don't find in most other first-world countries. Not sure what the origin of that is, but it is certainly due to a multitude of factors.
But lately, I seem to recall there was an Eminent Domain case somewhere in Connecticut a couple years back, where the supreme court upheld the town's right to wrest property from its owners, only to give it to a developer. This was all over the national news, and basically what amounted to "mobs" forced city councils all over the country to pass "resolutions" essentially limiting their own powers of condemnation.
Even if the SS hopes to not use eminent domain, it may have to; even if it doesn't, the threat of condemnation is likely the only thing that will bring some property owners to the table. Regardless of whether these people actually even get paid well above fair market value for their properties, the press and the public still enjoy drama and sensationalism and will not hesitate to paint this like "the big mean South Shore is trying to stick it to the little guy." In an environment like that, there may very well be some folks who refuse to sell.
This is a legitimate, undeniably public use of the power of (or threat of) condemnation: transportation. But by and large, the public doesn't care; it still looks like the Big Bad Government up to its Evil Ways again, trying to screw over all the regular Joe Schmoes who are just trying to get by... in the worst way possible, by stealing their Home!!
Another interesting phenomenon is that road widenings require similar property takings and happen all the time, and though they receive some press and some opposition, inexplicably there always seems to be more push back against transit projects than road widenings. I guess perhaps that's because everybody drives, and understands the need for road widenings, but NOT everybody takes the train. This is why basically every transit projects that has been built over the past few decades has been built in freeway, road, or railroad rights of way. There is a very strong negative public perception of forcible private property takings for the sake of transit. Very few politicians are ever willing to go on record in favor of such plans, for fear of retaliation at the next election.