Since Iowa Pacific only provides the passenger cars and some onboard staff while Amtrak provides conductors and engineers and as I understand it, the state of Indiana pays for the operation it is probably not Iowa Pacific's decision to reroute the train.
I don't know if there's an existing track connection from the current route to the South Shore or something would gave to be built.
The South Shore line doesn't operate into Union Station it uses a different one shared with Metra's IC route so Metra and the agency that operates the South Shore might not allow a diesel powered train on the line even if it currently only operates three days a week. The electrified tracks have frequents rush hour service and the non electrified parallel tracks has a lot of BN and CN freight traffic so it may also be congested and they might oppose more frequent daily Hoosier State service.
Is that the one that the City of New Orleans uses (St Charles Airline?) and has to back into Union Station?
I don't know about New York but how would they operate from LA to Long beach? The Alameda Corridor is pretty busy and may not want a passenger train. Also it's in a trench most of the way so not very scenic. I don't think it's got much appeal for tourists.