The Visual Studio 2017 Community Edition installed on the end X machine (10.105.0.31) said my license had expired (it should be free), but I was unable to log into my account to renew it. I ended up reinstalling TwinCAT and selecting the option to install the Visual Studio shell as well, since that comes with TwinCAT and does not require an account. I was able to open the solution in that and run it.

The machine at the corner station (10.105.0.27) only had the shell installed, and I had no trouble with it.