Product review (5 stars): did the trick
Solved our problem - now we get more than a trickle of water out of the dispenser and it's making ice like the day we bought it - and it was an easy fix.  (Wasn't easy to isolate, though!)  Had to cut the connectors off the old tubes.  It seems the housing in the back wall of the fridge is one-way - I was able to insert the new cables through without any trouble but I could not pull the old cables out.  I do have to say the cable from the filter housing to the pump (vs. the cable to the water supply) was a tad short so I had to bypass one of the cable guides.  Not a big deal, though.