Jim Dandy: my other cat (who died last year) used to do the exact same thing!! I know exactly how you feel, it used to drive me up the wall. I honestly dont have any tips though because I couldnt get her to stop. I had her for about 14 years, she was about 16 when she died & she started pooing on the floor after Id had her quite a few years. She used to wee on the litter tray & then go & find somewhere in the house to poo!! She even used to come in from the garden to poo! Infuriating...I just thought she was going senile or something, but my other cat who I still have is about 16 now & has never done it once.
Im sorry I cant help because I really do know what its like.
Hope you have better luck than me.