Any thick mudpit that is deep enough for a proper sink will probably be trouble getting out of without something to pull on.
I like to get in this kind of mud, but I will need a rope or pole to pull myself out, because when armpit deep in thick stuff, (like clay) there's no way that laying on my back will help (even without suction). If there is something sturdy to tie a rope to, I would bring a climbing rope and harness, but I like to tie the rope to the straps of my lifejacket instead, so falling tugs make the lifevest tighter. However, difficulty getting out is part of the fun! (I struggle in quicksand on purpose to sink deeper and get more stuck) Especially if it's a sticky sucking kind.
Sometimes if I am going to have a lengthy mud session, I have it trap me on purpose, with things to hold me down.
If the mud doesn't have a strong grip, I can usually climb my way out like normal. If it does have a strong grip, (and I'm armpit deep) it will take awhile to get out. I wear a life vest over my rain suit mainly for the fetish (and for balancing how deep I sink).
My escape technique will force me deeper, but sometimes the life jacket can prevent that. (Not always, due to the thickness and suction of the mud, this technique can still force me and my lifevest down sometimes, this can also make for a more interesting sink as I hold my arms up to take the challenge of keeping my nylon rainsuit sleeves clean, so I never reach into the mud even if the mud is to my neck, also making escape more difficult.), but the lifejacket helps keep me between armpit and shoulder deep, which is perfect depth for my fetish, perfect level to remain stuck at.
Usually the escape isn't that much of a problem though, the mud pits I have been describing are ones I can no longer go to, but the 4ft deep clay-mud-silt pit by the oregon millpond I still go to (I can share this) can be sticky, but is very easy to loosen up.