Ok, I've been working on this more. I decided to create a brand new project using the exact steps in the quick start guide. Copy the files from the zip file into a new directory, double-click the sln file, and open the main form. Now, after I build the project, only a few drivers show up in the toolbox. After multiple attempts, restarts, and a reboot, I'm still missing most of the drivers. I just get Pointer, OpcDaCom, SimulatorCom, and TwinCATviaTCPIPCom under "AdvancedHMIDrivers Components".
So, I went back to my original project that's already talking to a CompactLogix and re-added the EthernetIPforSLCMicroCom driver, renamed it, changed the IP address, saved, and it worked this time. I have no idea what happened to make it start working.
Edit: I just saw the pinned post about missing drivers being a known bug in VS2015. I'll work on getting a newer version downloaded. I'll have to do it from home, though, because our internet connection here is barely functional.