While working for Utah Power & Light as a home economist, I learned that the nasty film is from old grease from previous cleanings. From the very start treat the bottom of the pan as you would the top of the pan - clean thoroughly. If doing by hand, use CLEAN dish pan water and detergent. Better yet, do the pans first when washing them.
If your pan bottom doesn't have many grooves, you can use elbow grease and a soapy 3M Scotch Brite pad (tougher than others). It has worked for me over 40 years!