I used a pressure washer and removed all the black sealant on the pipe just outside the trap. Then I pushed it up the drain as far as I could, lots of fat deposits and stuff clinging to the pipes came off. I am going to buy a sewer hose attachment for the pressure washer and run it all the way along. I suspect the blockage is because not enough water is flowing into the trap to clear it, plus gradual silt deposits resting at the bottom of the trap.