Anyone ever check out Paonia Reservoir in west-central Colorado? It's a reservoir on the aptly named Muddy Creek and the surrounding hills tend to put out a lot of sediment. During late summer draw down, it exposes a lot of good looking mud. It's pretty much all without easy view of the road, so naughty business would be tough, but could still be fun for some sinking/quicksand play.
I drove by it two years ago, the lake was not as low as it is now with the withdrawal of all the water to try to keep the Lake Powell generators operational, however, it was quite muddy at the upper end of the lake. To me, it looked rather sandy and full of gravel and I suspect you could walk on it. Now that the lake is much lower, there could well be better mud down towards the dam. The real problem is that that would be really cold mud even in the summer...
Access is manageable even though the highway overlooks the lake. Just bring a kayak or some such and access the mud from the water, no one would think all that much about you "trying to get your kayak unstuck"...