To answer your question as to how loud the noise is, I would say that it is very loud and is coming from INSIDE the printer.
Thank you for sending me the instructions for cleaning the All-in-One, but none of those include the area where the problem is coming from. The only area it includes with moving parts is the ADF and that is not the problem here. I am not using the ADF when the problem is occurring. Would the need to clean the print heads cause squeaking? I don't believe I have ever encountered that before. I clean them every so often anyway.
Also, the problem seems to be getting worse. Although, it doesn't seem to effect the function of the machine much, it now squeaks no matter how many pages I print. I say that the function is not effected much, but I do believe it is slowing things down just a tad while printing.