Having worked for the State for 14 years in the past, there are better things to do with your time besides wait for anything that would appear to make sense, such as staring at a clock to see if you can actually see the hour hand move.
It took mine right about a month to change from packet mailed to processing application. I would say you could expect the same any day now.
See what I mean? You took your class and mailed it before I did, and yet mine says application processed. Makes no sense. Like I said before, be glad you aint waiting for your CHL in Washington DC, or illinois. Those folks have a looonnnggg wait!
Its entirely possible too that your application is being processed as we speak, and someone just forgot to get the info to the site.