We have the same problem with our 5 year old. Just like OP's son, he also has two older siblings who were potty trained without my really doing anything. We were very relaxed about it for a long time, but this has been going on for such a long time now, and we are getting worried that he is still going to have this problem when he starts school. :(
Just like the OP's son, our son will consistently go to the toilet when naked. We never used pull-ups, but have let him be naked a lot when he was younger. Cleaning poo from clothes or floors doesn't really bother me, he never really pooed on the floor, though. I thought he would learn to recognise the feeling of having to go if he had enough successes through being naked at home, but it has never changed.
We tried charts last year (after pressure from his kindergarten), it made him a little bit more positive to the toilet, at least he stopped actively hiding away when he was having a poo, but it didn't really make him go on his own initiative. He never really saw the point in the chart and wasn't very interested in getting stickers or rewards. He didn't seem to feel that he had any control over the "outcome". ;)
We have become very good at recognising the signs that he needs to go, and after using the chart he would usually agree to try to sit on the toilet. But it didn't make him understand that he needed to go. We have not continued using the charts as we are a bit sceptical to that approach.
We have also tried not asking and not saying anything, but this has had no effect.
What has been working best for us for quite a while, is to put him on the toilet after his afternoon meal, because he usually poos very consistently at the same time every day. We do not ask, because he will say that he doesn't need to go, as he doesn't want to stop whatever he is doing. We have him sit for ten minutes - in our experience it takes that long for him to relax enough to actually poo. We let him play Angry Birds or read a book, and I stay right outside the door, without talking very much and without leaving because he won't sit for that long if nobody is there. We don't force him if he really insists that he doesn't want to go. We have bought him a comfy toilet seat, and that has also helped.
We have periods where this works really well, and he even goes without being told sometimes, and we think it is over - and then we have periods where something has upset the routine and it is back to the beginning again, like now. :( Then he doesn't even go every day - it seems like holding it in has become automatic when he is a little bit stressed, and he is very easily stressed...
He still says that he doesn't know why he poos his pants so much, and that he doesn't feel that he needs to go, and he is sad about it sometimes. He has been very upset to realise that most of the younger kids in kindergarten don't poo their pants. So even though we try to create as little stress as possible around this, it is still stressful for him.
Once he has even become really constipated to the extent that he was screaming with pain. :( Now we have a laxative that we give him every time he doesn't poo in a couple of days. Letting him sit in a warm bath for a long time also seems to "loosen things up", he often goes straight to the toilet from the bath.
We feel like we have tried "everything". My consolation is that my niece had a similar problem and it suddenly went away.
Like OP's son our son has some sounds that he still doesn't pronounce correctly, but his language is very good and he is a very smart, intelligent boy.
I am wondering if it is a sensitivity issue. He is extremely sensitive to clothes in terms of itchiness, hard seems, not a perfect fit etc. and very sensitive to noise, people etc. He needs things to be quite calm and tidy. I wonder if the feeling of pooing is uncomfortable for him, and he has an automatic response to try to avoid it. He has always had some aversion to being dirty or wet.
I used to believe that potty training was very simple unless you did something "wrong", but now I know better.