We are in a similar position with our 6 week old, and as you will have seen its not easy!
E - Let them eat for a bit then wind him (sit him up), try singing, playing with his hands anything to keep him awak.
A - Change his nappy, sit him up, as soon as he begins yawning he should be ready
S - Swaddle him nice and tight, if you think "he wont like it I have tried it", I would suggest trying another blanket, or a miracle blanket. I thought Phoebe would hate it, and yes she didnt like it much at first, but she soon calmed down.
Then sit down and place him into your shoulder or if necessary slightly away from you , patting his back (near the shoulder blades), and shh loud over his crying (the shh needs to be louder than the cry to work, and yes I know its scary how loud you have to shh). Make sure you have a drink handy as your shhh will cause your mouth to dry up.
Be prepared to shh for upto 15-20 minutes. Phoebe cried and fussed, rubbing her head on my shoulder, fidgeting, if you have a spirited/touchy baby they will really fight the blanket at this point! After 13 minutes she stopped almost completely and just lay there and went to sleepy mode.
You then put him down in his cot still patting and shhing. Then continue the shh and pat until the rem stops, it could be 20 minutes, he might wake up at first carry on shh/pat unless he screams for more than 10 seconds or so, sometimes they do cry out and stop quickly. If he screams for longer then pick up and start again, you should find it takes less time to get to sleepy mode again.
Now if I were you I would expect to be there for at least an hour trying to get this sorted at first, it will be worth it.
However I will say that I havent as yet done this to the end as I only tried yesterday and we were all too tired (phoebe hadnt slept in 10 hours), so I do know how you feel! But we got to the point of getting her to go down and asleep on her own in the cot (just getting this far seems like a breakthrough right now), so I know it can work.
Lots of hugs let us know how it goes,
Simon