P0783 = 3-4 gear shift error code
P0720 = Output speed sensor circuit malfunction
P0722 = Output speed sensor-no signal
P0303 = Cylinder 3 misfire
P0306 = Cylinder 6 misfire
I don't show a code P0316
Here's a handy code listing for the 700 numbers...you can select all the groups from that webpage
P0700 to P0799 listing
All the transmission codes could be caused by a defective output speed ssnsor. You might want to do some googling to find out how to test the sensor.
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Joe & Shelly, Justin, Tyler, Alyssa | Butler PA
2008 Tiffin Allegro Bus 43QRP|Cummins 425|Honda CRV