Hi, Brian;
if you read Klaus' last post in this thread, you'll see a good suggestion on how to clean the head. As you replace the gummy wheel, you'll see that the magnetic head has its surface completely accessible. This way you can clean it with isopropyl alcohol, commonly used to clean magnetic heads, or, if the head is too dirty, you can use a cotton swab soaked with a small amount of metal polisher. I had to do this once, and only once, with one of the HP41 card readers I have (82104A) because it had a kinda brownish dirt on it (metal oxide), and these metal polishers are abrasive as well. Anyway, after the cleaning procedure, the swab had its surface partially covered with a big black spot from the residual metal oxide. This so mentioned card reader works perfectly fine till today, about three years after having its head cleaned, and I use it a lot. No extra cleaning was needed, and it reads, writes perfectly fine.
If you feel your card reader needs such 'in deep' cleaning and you feel yourself confident enough going ahead, do so very carefully, and use the swab gently. And remember searching for the finest, less abrasive metal polisher you can find. The one I used is named 'Brasso', and it is likely to me that the name comes from brass. Maybe there is a similar product where you are. I succeeded cleaning many magnetic heads in tape and cassette recorders, and it seems to me that good results were also achieved by others when cleaning the magnetic head of HPIL tape drivers.
Hope you succeed.
Cheers.
Luiz (Brazil)