You can gently unlatch him as he drifts off, if he latches back on then let him but then unlatch as he drifts off to sleep. Keep doing this and eventually he'll go to sleep without a nipple in his mouth. It is a bit of a competition of which of you gives in first though!
I was a bit like you and DD was on the boob all night, got to 13 months and I needed to go back to work and drive to get there and just couldn't do it anymore. Did sleep training and within a week she could just go down to bed and off to sleep. With DC2 did sleep training at 9 months.
I would say, people have strong feelings about sleep training and I'm not necessarily telling you to do that right now, but it is easy as a first time parent to perceive any crying as meaning the baby is distressed and that it must be terribly damaging, whereas sometimes a bit of a cry is more about being pissed off. Not the same as being scared or distressed.
Your son has learned that the procedure for going to sleep is being on/next to you with a nipple in his mouth. If he wants to sleep and these conditions are not available, he'll scream because he thinks he needs that to sleep. You can gently nudge him into other habits, maybe by delaying feeding a minute or two, patting instead of picking up etc. If you're not desperate then you can move in that direction rather than doing regimented sleep training. There's a book on Gentle Sleep Training by Sarah Ockwell Smith that might help.
Of course it will get easier. You don't get many 3, 4, or 12 year olds that do this! However if left to his own devices I'd imagine he'd be in with you and feeding past the 12 month mark, more like 3 years to want to be sleeping in his own bed of his own accord, from what I've seen with friends.
It can help to get them to sleep then put them down after 5 minutes or so, when they're deeply asleep rather than only just asleep. And put hand on their tummy so it feels a bit like they're still being held. I also used to use an ergosling and DC would nap on me at that age.
Ultimately I think today's parenting styles often go too far in being child-led, gentle etc - you need to find a set-up that is a good set-up or compromise for the needs of both parent and child. Sometimes we think 'oh baby wants this so I must do it even if I hate it'. You're the adult, you set the parameters for what happens, baby needs sleep, baby might want sleep on you with nipple in his mouth, but if this is going to make you exhausted and resentful then maybe this want can't be realised because the price is too high.
Your mood and stress levels etc also impact on the baby, it's all got to be weighed up and if the way you do things now doesn't work for you then make a change and stick to it, ultimately he's a 6mo and doesn't get to control the whole shebang! If you started putting him down and patting, shushing etc then eventually that would become his new routine. But you probably won't get there without some degree of baby being annoyed and crying a little.