I told him that we would have to put him in pull-ups hoping of course that the threat would convince him to go to the toilet but instead he rolled his eyes and got some pull-ups from the drawer.
That's fine - part of the two-strike rule is giving him a choice every morning. You need to change your thinking - don't see pull-ups as a threat - they are a legitimate choice for him to make or they are a natural consequence of his behaviour (so still a choice in a roundabout way). They are not a punishment.
Put a pile of pull-ups in his drawer with his pants - when you are getting him dressed in the morning, get him to choose. If he chooses pull-ups that's fine.
No matter what he chooses, remind him that we do wee wees and poos on the toilet and then in the normal course of chatting to him while he is getting dressed, ask him it in the form of a question ("where do we do wee wees and poos").
Do some positive re-inforcement "Let's see if we can have no accidents today".
Regularly ask him throughout the day if he wants to go. If he says no, sometimes accept it, sometimes say "well lets try anyway" (although if he kicks up a fuss, don't push it - it's his body).
If he is wearing a pull-up and you have to change it because it is wet, do a little gentle chastisement followed by re-inforcement "You silly banana, you've done a wee wee in your pull-up rather than the toilet". If he's in the pull-up through choice, rather than as a consequence of the two-strike rule, give him the choice between pull-ups and pants again.
Don't ever get cross, but don't ignore it either. DD2 is younger, but when she has an accident I use lots of words like silly banana, daft monkey, pest etc or just "Oh dd2, what are you like", although it is always used very gently rather than a cross way.
If he does go to the toilet either voluntarily, or produces at the times you encourage him to go, obviously re-inforce it with a lot of praise (but not treats) and don't punish accidents by removing something ever.
I suspect that it has been going on for so long that it has become a battle of wills - he probably feels like it is something that is being 'done' to him, especially with the distress of the night-time accidents and the intentional soiling could possibly be his way of exerting control.
By doing it this way, you are putting him back in control - he gets to choose pants or pull-ups, he gets to choose whether he goes to the toilet or not. If you do not show that you are bothered by him wetting himself, he will very quickly realise that the only person who is inconveneinced by it is himself.
It also has the added bonus of removing the stress for you.
Give it 2 months - if he's no better, go to the GP, but I honestly think if you do it this way, you will be surprised by how quickly he gets it.