It turns out the trailing slash in the PublishDir property is escaping the end quote. Escaping the trailing slash solved my problem.
/p:PublishDir="\\BSIIS3\c$\DATA\WEBSITES\benesys.net\benesys.net\TotalEducationTest\\"
This way we can use quotes for paths that have whitespace in properties that MSBuild requires the trailing slash.
I know this is an old post, but I feel like I needed to share this with someone 🙂