Deploying dotnet core to Heroku
I finally got this successfully deployed to Heroku, it's all up and running. Tseng was a huge help on this, so thank you. My buildpack that I was using was targeting an older version of .NET Core. Heroku has an experimental buildpack targeting ASPNET5 here: https://github.com/heroku/dotnet-buildpack.
As of the time of this answer, this buildpack is using Mono for runtime execution. There is a pull request to use the .NET CLI that I used and it works great. It can be found here: https://github.com/noliar/dotnet-buildpack. Hopefully they accept this pull request soon. This was the buildpack that I used.
Hope this helps someone.