Oh no im sorry you had such a rubbish night

He was possibly really OT at 4.20 so when he did wake it was too much for him.
It might well take a few days of doing W2S consistently before it really works for you...... but im not entirely sure as i think i was quite lucky with my lo. If you are not too tired tonight, might be worth another try, it is good that he didn't fully wake at 5.20 and 5.40 even though he was still crying out.
I don't want to throw too many ideas at you at once, but something else that you could try when you feel ready is introducing a lovey. I just gave one to my lo about a week ago, to try and help wean him off the swaddle for daytime naps (he doesn't seem to need swaddling at night for some strange reason), and i have to say that it really seems to be working and if he wakes early from his nap he is able to use the lovey to self-soothe back to sleep. But it is only in the last 2 days that he has been able to do this, the rest of the week has been a lot of going in and resettling. What i have done is give it to him to hold at every naptime and night time so that he starts to associate it with sleep. It could be that your lo is using you and the BF'ing as his lovey to help him get back to sleep, especially if you don't think he is waking due to hunger.
Going to keep my fingers crossed for you, also sending a big hug. Hope it goes better for you tonight.