I hope that others will contribute to this thread as time goes on. The first thing you can do to harden your server is make sure that you are using the highest version of PHP. The higher the version - the better. 

UNA is a content management system and competes with others. The more popular it becomes, the more malicious and frequent will become the attacks. Thankfully, UNA is well written with regard to security.

My site has been working fine now and hopefully all the altered files and back doors have been removed. I'm still watching it every day, knowing that one line of code, even added to certain image files - can mean a re-entry.

Special thanks to Leonid S who helped me unravel my problem.