After this experiment, we’ve proven to ourselves that using a dishwasher is not the most water-effective way to clean dishes, which is what others (like the Phoenix Ecohood) already made known. Our fairly new dishwasher requires 8-10 gallons of water when using the most conservative settings, and up to 13 gallons when using extras. But we still use it, and capture the graywater for our pit. When the water is captured, we use Seventh Generation Dishwasher Gel.
Another reason to not use a dishwasher is because virtually all dishwasher detergent has sodium in it, and you don’t want sodium to build up in your soil. So obviously we are making a compromise.

The basic technique for our water capture is manual. Under the sink, the dishwasher outflow connects to the kitchen sink garbage disposal as shown.

When capturing the water, we loosen the hose clamp and put the outflow hose into a bucket. You might notice that it is a 7 gallon bucket. This means that when running the dishwasher in this mode, we need to stick around the kitchen and after a couple dishwasher cycles, empty the half filled bucket so it will not overflow.

Some may consider this a bit inconvenient, but it avoids a messy and expensive replumbing job.