An abandoned silo might be targeted. If it hosts some sort of ABM program even more so.
I also never expected the project to build a sub, maybe a large freighter capable of launches, but not a sub. I thought of having the Red October captured by the CIA in my game world. Since the Project has some aspects of a reverse
Glomar Explorer in my game (industrialists asking for help from high level CIA officials), I thought that the sub, rather than being scuttled, could be used as the base for Satellite launches. This allows a equator launch which helps orbital insertion and avoids serious polar magnetic interference. That is also why if I chose an island it would the the ones off Costa Rica from the Jurassic Park series.
As far as the island in the great lakes goes, I have now decided that one of the industrialists will fake a assassination attempt and then declare he is buying the island and living in protected seclusion (maybe a little Howard Hughes comparison). The construction of his mansion will cover the construction of a high altitude balloon based communications center for the Midwest and East coast elements of the project.