I just moved to a different state and lo and behold, I think I've found the Holy Grail. It's within walking distance of my house; just over waist deep with thick, creamy dark tidal mud/clay. Not too many insects and it's secluded. Cleanup during the daytime can be a little dicey because there is absolutely no way to rinse off and get out without getting a thick coat of mud at least up to your thighs. At night you can sneak across the road where there's a pond for washing up. There are some sticks/debris, but once you clear a spot it stays nice and the tide washes away your footprints every few hours. The mud itself is just the right thickness, consistency and color, at least for me.
Here's one spot closer to shore that I use when the tide isn't quite all the way out yet. It's a bit thicker.
Once the tide goes out a bit more I can move out further. This is a picture of the entire mud flat, which is quite huge. The tide is not totally out yet in this pic so it doesn't do it justice. It's got at least another foot to go. Once you get out there and roll around a bit to disburse all the surface water it turns out perfect!
Now I just need to find some nice lady to enjoy this with me to complete the perfection!
Congrats on finding us and that spot. 
nonetheless looks like an interesting place