Hi Brad. I am so sorry you're going through this. You must feel overwhelmed and helpless. You have my sympathy.
Have you considered the possibility that this child has a personality disorder? (By the way, I am not a child psychologist, I am only drawing from reading lots of literature and personal experience.) You have described pathological lying; manipulation; anti-social behavior (in the sense of wanting to be alone); stealing; and most importantly, constantly pooping himself. I really hope this doesn't upset you, but your post screamed "sociopath" to me. The signs of sociopathy begin in early childhood and a couple of red flags are bed-wetting and hurting animals. You don't mention the latter, but I wonder how this child is around pets, animals, babies, and "weaker, smaller" living things in general?
Unfortunately, doctors and psychiatrists are far less likely to recognize this than you'd hope - sometimes because the child is so adept at lying and manipulating, sometimes because the practitioner might not be very well versed about the disorder (for example, he or she might not know that sociopaths are very rarely "serial killers" and they're not always violent. The key is lack of remorse for wrongdoing/lack of empathy).
It's not so unusual - it's actually estimated that one in 25 people has this disorder, so there's a chance that this could be the issue. Martha Stout, PhD. cites that statistic in her excellent book "The Sociopath Next Door," which has several chapters (real case studies) on child sociopaths. I highly recommend taking a look at that book or anything that Dr. Robert Hare has written on the subject.
https://www.amazon.com/Sociopath-Next-Door-Martha-Stout/dp/0767915828
While googling around after reading your post I also found this:
http://www.medhelp.org/posts/Child-Behavior/Is-my-child-a-sociopath/show/699541#post_answer_header
I hope that my hunch is way off, and I'm truly sorry if anything I've written has upset you. But please trust your instincts that something is wrong, because while having "accidents" isn't always indicative of something alarming - and can be grown out of - and neither is lying or stealing - the specific cluster of behaviors you've described as opposed to one or two behaviors in isolation is troubling to me. I'd say start writing things down, educate yourself (better to know a lot about this and then rule it out than to miss it), and find a child psychologist with specific experience in this field. Most others will miss it.
Good luck. And kudos to you for persevering even when the other adults in his world, professional and non-professional alike, won't.