My son went thru this unpleasant phase at about the same age. It's just something they find fascinating. I was beside myself too when I was advised to end the behaviour by cleaning him off in a cold shower. The next time him got in his poo diaper I took him to the bathroom, turned only the cold water on in the shower and (standing with him on the outside of the tub leaning into the shower) let the water run on his hands and arms til everything was rinsed off (poo n soap). I explained it had to be done this way b/c he could get really sick from having poo on his hands and we had to make sure we got him really clean. He was upset by the sound of the shower and the cold water, and I felt like such an ogre doing that to him, but he NEVER played in his dirty diaper again.
I am glad that you have not spanked him or yelled at him as that would not help and probably make things worse. Unfortunately, you cannot rush this. There are plenty of posts of parents with 3/4 year olds that still have potty problems.
Got a feeling that the problem is that you are a bit overwhelmed with the activity level of your kids. If all you had was him, I am pretty sure that you would have noticed the smell or him taking off his diaper and would have dealt with it before it became a big mess. However, that is out of the question now. The real problem is as you say, " I'm ready for him to be done with diapers." Unfortunately, he is not.
I would suggest noticing the time of day that he poops. Then at about that time take him into his potty and sit with him. Perhaps read to him? If he does poop. Make a big deal and reward him immediately. If the timing is right, your extra attention should make this attractive to him.
So far your instincts have been correct about how to handle this. Hopefully, some of our other posters will have more ideas. Good luck and let us know how this works out!