I havent tried so myself, however perhaps set the backups for this client to be independant and disable full and incremental backups so that the server doesnt do them on a schedule. Then write a .bat file in windows to execute the command to initiate a backup from the client. If you do it from the client, i bet the &USERNAME% context would work.
This is all speculation!
Or, you could also script a robocopy of logged in user’s folder to C:\windows\loggedinuser\ and have urbackup backup C:\windows\loggedinuser\