Hi Scarlett - just reading your post a few things suggest themselves to me... bearing in mind I have no experience of 6 year olds as mine are too small (and I had a hideous, hideous morning with DD so not exactly feeling confident in my own parenting skills...)
I would hazard a guess your DS isn't feeling listened to and hitting is the only thing he thinks you respond to. Therefore "hitting is right" because it works, in terms of getting a reaction. He seems to be trying other tactics to express himself before hitting, the dawdling etc are sort of ways of telling you he's not happy, and sure, sometimes/often you can't do/get what you want, but perhaps you could acknowledge his feelings so at least he feels you understand his frustrations, before he reaches a point where his frustration is boiling over into violence?
E.g when your DS said - "I want to watch TV when I get home!", could you have a) asked why - or find out if there is something on that he especially wants to watch?" (Are his friends talking about a specific programme and he's feeling excluded, perhaps?).
B) given a reason why he couldn't watch TV - "I know you want to watch TV but I'm sorry that we can't do that tonight/when we get home because . Perhaps he is feeling that the parental power is being wielded unfairly because he doesn't understand why he can't watch TV and it seems a bit arbitrary?
C) acknowledged his feelings, acknowledge that he can't do what he wants to and suggest alternatives? "I know you want to watch TV, it's frustrating isn't it, when you want to do things and you can't? I get frustrated that I can't when I get home but I have to , unfortunately there are things we have to do when sometimes we want to do other things. How about we watch a bit of TV later/play a game/suggest compromise or negotiation you as parent are happy with...
When he kept repeating himself and not crossing the road, instead of giving him more time to calm down, it's effectively giving him more time to brood on the unfairness of it all. Rather than getting it out of his system, it's simmering away. You say the only time you got confrontational was when you'd crossed the road, but I bet your son didn't experience the situation like that - for him it was a confrontation from the off. Could you/did you acknowledge he's cross, rather than playing with your phone and ignoring him? (Can you remember a disagreement you've had where the other person ignored you and what that felt like? It's quite a passive-aggressive thing to do, winds me up anyway, and your son is reacting to passive aggression with aggressive-aggression. Probably because kids of his age haven't sussed passive-aggression yet, so don't have those sorts of tools at their disposal...)
The rest of the journey home seems to be him trying to find a way to communicate his feelings to you in a way that gets you to acknowledge them, he's tried a variety of ineffective (and annoying) ways to connect with you on the issue but you're not engaging with him - from the outside the issue is less about the fact you won't let him watch TV, more that (putting myself in his shoes) you don't seem to care that he's upset that he can't. I think it is getting across that you do care that is at the root of the issue, which would hopefully then head off the violence.
Anyway, that's what I would have done differently. You say you sulked at him after his flippant sorry (when he didn't appear to acknowledge how you feel about the hitting etc), well he sulked at you all the way home (when you didn't appear to acknowledge how upset he was about the TV watching) - it's not that different, really.
"I wanted our talk to have affected him in some way, you know? But no." - he wanted his behaviour to affect you in some way, get the reaction he wanted out of you -of course he loves you, but when you say no TV and take the impenetrable hard-line, ignore him etc, he's experiencing that as love-withdrawal in the same way that you say "how can you love me if you hit me?" - "how can you love me if you ignore me/my desire to watch TV/don't care that I'm upset about it" do you see what I mean?
That would be my take on it anyway. And I could be miles out.