The problem here is the lack of investigation into the problem, and fixation into thinking a statistical guess means anything.
Statistical analysis (boards ordered from JLC do not work as often, board ordered elsewhere work more often) is completely meaningless. I can start giving it some weight after we are talking about tens of thousands of boards ordered from dozens of different fabs and seeing large differences, and even then, it isn't proof of anything, just a hint. At this level, it isn't even a hint.
Need to investigate more. There is no magic sauce for this, it takes time and expertise.
I was once almost sure I have a manufacturing problem (PCB or soldering) because out of batch of 30 identical boards, a few boards failed to initialize an accelerometer. SDA, SCL or power must be flaky! Guess what? Pure software problem. All same ICs, software behaving 1:1 the same, some ST accelerometer units fail to work. Initialization sequence changed, now they all work.