I love doing decoction mashes. I brew with another guy so it makes the labor easy.
We bought a 2-quart pyrex measuring bowl and use that to extract the mash. "Thickest part" is an ambiguous term but there's a reason behind it. The grist holds temperature better than the liquid. So in order to increase the temperature of your mash, you want to extract as much solid material as possible; hence "thickest part". Too much liquid and you won't be able to hit your target temperature. Too much grist and you run the risk of scorching what you are trying to boil.
Have a calculator or brewing program handy when you decoct. You'll find that sometimes your temp will drop between phases and that will affect the volume you need to pull from the mash.
I also love decoctions. You can't get a really complex malt profile any other way. There is another reason for using the "thickest part". Once you dough in, most of the enzymes are extracted to the liquid. By boiling the thicker portion, you avoid denaturing the enzymes and keep a higher diastatic power in your mash.