Good stuff. When you drop the POP you usually need to reset the H & L speed needles, with the AutoTune you will just have to run it hard in some wood for the computer to reset.
EDIT: You didn't happen to notice or measure the size of the venturi while you had it apart did you? The reason I ask is that the carb is a C1M and is the same carb on the 445/450 and the 570/576. The only differences are the venturi size.
The 445/450 has the 11mm venturi and the 570/576 has the 13.5mm venturi. I expect that the 562 is running something like a 12-12.5mm venturi.
I'm running the bigger 570 carb on my 450. The 555/560/562 may be suitable for a carb upgrade to the larger 13.5mm carb.
You said the tuning block bolted on the side of the carb. Is the carb the same as a conventional carb or are there some extra holes for mounting bolts. If it is a standard carb, you can pick up the 570 carb for about $60.