Never done a deep fryer, but when I had to clean the popcorn machine (first time it had been cleaned in 5 years), I had to use razor blades to scrape off the hardest gunk, then use a scotch pad with Dawn. After 3 hours, it looked beautiful!
The deep fryers build up a layer of grease and bits that stick hard to the sides. The more you change the oil the easier they are to clean however good oil can last a while and isn't cheap. Nothing I've tried other than a good firm brush and some elbow grease has worked well. I've tried some heavy degreasers I've used at my job too with limited success.
Make sure to roll the silkies in milk, then flour, then egg and finally a good breading or breadcrumb. Delish.
you know, getting a good build up of burned on grease is DESIRABLE on cast iron and some other cookware.....can't see as it would hurt you in your deep fryer