I would sleep train rather than wean.
Putting him onto formula seems like it would leave you with the same problem but having given away the best tool you have for dealing with it.
Sorry I'm far from an expert here so feel free to ignore. When dd1 went through her phase of terrible sleeping I was so glad I could feed her back to sleep. Also feeding so useful for teething pain and comforting sick babies. I would be hesitant to give it up coming into winter.
I would put him in his own room. No co-sleeping in my house. I've seen too many haggard aunties with fractious children that slept in their parents bed until they were at school to have chosen that. Sounds like it worked for you with no.1, but a child who likes his own space might prefer it once he gets used to it.
There are tons of things you can try before cc would seem like the only available option - own room, new bedtime routine, nightlight (with music?), putting him down awake, dh going in rather than you. Whatever you do, consistency and firmness are key. If you want a baby to learn to sleep by themselves you have to teach them that rather than teaching them that if they wake up they get boob time.
I don't even know how you would do cc with a toddler. They need their sleep so much that opening up bedtime as a battleground seems awful. Better by far to get on top of the sleep thing now so they look forward to their head hitting the pillow when they are older.
Sorry not much help, op. I do sympathise. My dsis had 2 terrible sleepers and she and dbil are so tired all the time. I am enjoying this baby/toddler stage so much more than she is because my family gets up most mornings well rested.
I really hope you find something that works for you all and doesn't involve too much stress.