I'm surprised someone would claim their almost 20 year-old 'anything' are completely clean, but let's put that aside for now.
The gray spots on the mylar aligned with every stator hole opening are normal, and they're due to migration of the graphite coating which is manually applied during assembly. But there should not be obvious differences of these spots between two panels from the same pair. However, the 'spots' might be a red herring in your case, and you should be looking for the typical age-related slow failures:
a) ESL panel slipping down and hanging from the connecting wires
b) ESL sandwich separating due to loss of clamping force of the shrinking weather stripping, causing the copper charge strip to loose good connection to the mylar
c) charge strip corroded
d) HV supply problems
Let's rule out some simple things: Play the problem speaker and notice if squeezing the ESL sandwich together by hand at different points makes it sound different, or if it's louder from certain sections of the ESL, or if it causes (or reduces) faint squeeking (indicating a HV leak). If you get no changes, move to the next step:
Let the panels stay unplugged overnight, and swap the panels L to R, and check if the problem follows the ESL panel or stays with the power supply, and report back. While they're partially apart, tighten up every single screw inside and outside.
Good luck!