I just wanted to provide an update on what we actually decided to do to resolve the SFTP issues in SSIS. Here's the breakdown of what happened:
I initially tried using Putty and some batch files to upload files, but it was difficult to capture errors. Also, I was storing our SFTP credentials in clear text files since it was part of the Putty upload scripts.
We purchased a CozyRoc license for our SSIS server for a couple hundred dollars a year and I'm completely satisified with the results of using their product. With CozyRoc's product, the control flow task raises errors if there are any problems with the upload. Since I also have several junior SSIS programmers on my team, it was easier for them to understand how to setup the control flow task than to use the Putty scripts method. And finally, the password is encrypted using SSIS's native encryption for protecting sensitive data. I no longer have any passwords stored in clear text on my server.
I did review some of the other 3rd party libraries that were recommended in this question, but it appears CozyRoc was the cheapest of the vendors and they also had a few other SSIS tasks that I have been able to use in my BI team. Thanks, CozyRoc!