I'm currently inspecting every single inch of this machine with a flashlight. I haven't found any thread bits or lint. I'm also turning the handwheel slowly as I watch for moving parts. I swear I've oiled every bit of metal on metal (not just the red dot areas) but I guess I'm missing something. I'm also running it slowly with a blow dryer on it, not sure what that will do but I feel I have to do something!!
Anyway, wanted to add that the squeak would be more accurately described as a chirping. Hopefully that will be helpful. Thanks to all, I really hope I can fix this problem.