After a bunch of searching and many incorrect suggestions I found the right SSDT package to get SQL Reporting projects to work in VS 2015:

Follow step 3 here:
https://msdn.microsoft.com/en-us/mt186501

Everything I did to get SSDT installed through Visual Studio as many suggested didn’t work for getting me access to SQL Reporting projects. Installing the SSDT package from step 3 in that link DID work.