I just had this problem with a '97 Mountaineer. First it started with O2 sensor fault codes, so I replaced the front O2 sensors and crossed my fingers. For about 25 miles, I thought all was well - then the CEL lit up again with the "catalyst efficiency" code - which it was NOT showing before.
I was about to replace the headers and cat-back exhaust parts anyway, so I went ahead and replaced the front cats and the rear O2 sensors; did it all at once.
There's a good chance that fresh O2 sensors (front and rear) will fix this - and if that doesn't do the trick, you're not out any money - the new sensors can be swapped to the replacement cat(s) / downpipe(s). Try your idea first before laying out the cash for new cats (the "EPA tax").