That's a very good suggestion HappyCats, but I don't have a dryer!
That's the dilemna, buy a dryer just to remove cat fur?? And, I have no desire to go down 2 flights of stairs and walk a block and a half to the laundry mat just for that either! (That's why I bought a washing machine after a year because I was tired of washing the clothes and sheets by hand in the bathub!!)
I'll try the "cleaner apartment" method, plus more tape/lint removing and maybe change the food. I don't think it is humanly possibly to shave a cat.