How do I troubleshoot my generator and transfer switch installation?
I went to test it out again, hoping elves would've fixed it while I was gone, but no such luck.  As I was playing with the oil burner, I flicked on/off the emergency shutoff switch and got shocked.  This led me to check the ground wires.  The transfer station looked ok, so I went outside to check the power inlet.  I was cautiously happy when I saw that the ground from the building wire had come loose due to some really shoddy workmanship.  I reconnected and secured the ground and everything worked just fine after that :)

Thanks Tester and everyone else for all the assistance.  It was greatly appreciated.