2006 Vnl 13 speed transmission problem or injector

Flap down? You're talking about the range selector I assume? With the 13 you'd have to pop the splitter back first before dropping into low range. Are you hitting the splitter and then immediately dropping into low range?

 

If i remember correctly in the Eaton video you are supposed to pre-select the high or low gear range [move the flap] so in other words when your in 4th and wanting to go to 5th you would flip flap up the shift up....same coming down...5th to 4th...flip flap up in 5th then shift down. If i remember correctly they mentioned something about not selecting it in neutral as it can possibly damage the shift fork......besides, as per your CDL training you should not be coasting in neutral to a stop.
So if you want to do the coast to a stop make sure you range select before you come out of gear and at least clutch out of that gear into neutral and it should shift down to low range without grinding.

 

Second problem could be something as simple as a bad U-joint or as bad as a transmission issue....my recommendation is take it to a technician you trust and have them roadtest/verify the complaint then diagnose as drivability vibrations can get very costly so one is best not to guess.