I replaced my soil stack vent with an air admittance valve, but when I flush the toilet the water doesn't go away so quickly (only an extra 2 seconds, but the flow now isn't fast enough to clear the shit and some floats!) and also I can hear it pushing into the nearby shower drain. At the bottom of the soil stack is some water, as though perhaps the pipe running from there to the main drains is not entirely downhill. I assume it's creating back pressure. If I flush the toilet with the vent removed, it flushes fine. The toilet is only a couple of feet from the soil stack.
I had a peek in a drain cover just outside the front of the house, and there are two drains, one for waste, and one for the gutters. The waste drain is blocked, it's full of water there. And simply flowing over into the rainwater drain! How stupid! So I've been polluting the rain drains all this time without knowing. I guess I go borrow a big drain rod....