When I installed my new Panasonic Fan/Light/Nightlight I did not want it to get clogged up like you describe. I also did not want to take out the mot or every few months to clean it. I bought a sheet of 1" thick reusable fur nace filter material and cut pieces to fit in my grill. That worked out pe rfectly. Now I just remove the filters, wash them with soap and water and put them back in.
I installed two bathroom Panasonic fans (Fan only) for a customer several m onths ago who had a cat. The fans that I removed were caked with dander. I tried to use the same filter material that I used on my Fan/Light/Nightli ght but the space was too tight. I suggested to the homeowner that he try looking around for some other type of filter material that was thinner. Ma ybe even a screen would work.
One thing about installing a filter or screen is that it will affect the fa n performance. Bath fans are not designed to accommodate a filter. Havin g something in there will affect the air flow. However, based on my own ex perience I have not noticed that the fan is under-performing. It is import ant to keep the fan and filter clean. I should note that when I installed my new fan, I relocated it from the builder's position over the toilet. I installed mine over the shower which has made a tremendous difference in th e amount of steam removed. No more foggy mirrors.
I think that it might be more effective to brush the inside of your bath fa n air duct instead of just vacuuming it. I have a brush kit that I use for my dryer vent. It works for bath fan air ducts as well.
I wrote a 19 page booklet entitled "Almost Everything You Need To Know To R epair A Bathroom Exhaust Fan In Your Home". It is free to visitors of my w eb site. In it I list every bath fan manufacturer's contact information fo r obtaining replacement parts.
John Grabowski http://www.MrElectrician.TV