Cannot re-install Visual Studio 2017 Community integrations

Previously, I had a fully working CUDA Runtime 9.0 + nSight 5.4 + Visual Studio 2017 Community. For reasons unrelated to NVidia or CUDA, I had to uninstall VS and re-install it. Following this, I am unable to re-install CUDA; the installer gets an immediate error message no matter which components I check to be installed.

I was able to get the CUDA runtime installed by manually copying some files from my previous installation, but the Visual Studio integrations are still missing. Even if I start the NVidia installer with only the Visual Studio Integration selected to be installed, I get the “NVIDIA Installer failed” message, with no further indication of what the problem is.

How can I get the installer to re-install the Visual Studio Integration (and any other missing parts)? Without this, I cannot build my C++ project, which includes .cu files.

64-bit Windows 7 Pro, Visual Studio 2017 Community, CUDA Runtime 9.0, nSight 5.4, GeForce GTX 1050 Ti