1377 red dot problem

Sight height alone would not explain a 6” discrepancy.

The angles at play here—those of the barrel and the sight’s compensation—are so slight that it’s not practical for the layperson to measure them, and a laser boresighter would be next to impossible to use on a 1377. So…as a practical matter, I would say the best and perhaps only option would be to try another sight (red dot or scope) and see if the problem persists. 
 
I’ll send it back and try another brand.

I have had good results with the sig sauer romeo 5 reddot, on my ar15, and on my sig virtus pcp rifle. They mount good hold zero, the dot brightness is adjustable, for small profile. The sight comes with 2 mounting plates, one low one co-witness. 
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Not the cheapest, but a good choise. 
 
For what it’s worth, I have 3 different cheapies in the $20 - $40 range and they all work perfectly well. 

The only issue I can speak of relates to their use of opposing grub screws to lock in the windage adjustment. While zeroing, tightening them to the “leaving it here” torque shifts the POA very slightly, making a bit annoying to get set up for a precise zero. Some people would probably not even notice. For those that do, it’s just a one-time thing so not really a big deal. Otherwise, the adjustments all work fine and have enough travel for zeroing anywhere in the 10-30y range at least.

Bear in mind it takes more adjustment range to zero at a close distance like 5yds vs 10yds.