...the eye is straight...
This is a good idea to check,however, check the manual though. My machine's manual specifically say
not to be straight on, that you want to have a slight offset. Doesn't matter which side, but to have a slight offset. May not be the case with the OP's machines, but just to be sure to check.
Could also try slowing down as well. That's just a stop gap though to try to get through. If you are running really fast, and the needles are bad or getting bad, that could cause it as well.
As far as lower tension, I would check it first to see if it's holding. Adjust accordingly if it isn't, but do so carefully, once you get the lower tension out of whack via adjustments, it's hell getting it back just right. If it's not holding tension, swap it out.