Thanks. I came across that article at one point but I'm not sure why that would be the same issue since I can run it just fine in SQL Server 2012 on the remote server that the SQL task points to without entering any additional credential parameters into the query.
For whatever reason, I was able to ultimately work around this issue by changing from an SQL task in VC to an "Execute" (cmd shell) task and using the "Command:" input "sqlcmd" with the proper arguments. Exact same code just, running directly in a shell.