Don't know if this is the right way, but its what I do: I do the Garry Dean method on my truck, so I use three gallons instead of two, and usually I have a quart or two of clean hooch left over. I wash the rags immediately after I'm done, while they are still wet and the crud hasn't had time to set.
I put the left-over CLEAN rinseless wash in the washing machine with the towels. I put in the towels with regular laundry soap and a bit of vinegar. Not too much of either. My wife isn't brand loyal, so it tends to be "Brand X" soap.
I run it on "heavy" on our Speed Queen machine, which is a pretty brutal wash cycle. If I am around, I'll set the clock back and give it maybe twice as long as normal on the "heavy" cycle. When the machine stops, I increase the load setting to give it extra water, and run it through again with no soap, but another smidgen of vinegar on the wash cycle. Cold water only, of course.
Some of the cloths are stained, but they are perfectly clean. As long as the weather is cool, I'll mix up a new bucketfullof rinseless hooch, put most of the damp towels in, put a lid on it and store it in the garage until next week. That way I save drying costs for the towels. (I've found with the Duragloss rinseless, anyway, the stuff will go sour if you don't use it for a couple of weeks).
I find I can pull any towel from the pile, dry it and use it to clean my eyeglasses, so I'm fairly confident they are clean.