Hi OP, I'm in the exact same boat as you. You're not alone, I know how exhausting it is... I'm afraid I don't have any practical advice. I exclusively breastfed my first born and fed her to sleep until approx 10 months I think. Eventually it stopped working for me as I was exhausted feeding her back to sleep when she was just waking multiple times in the night for a comfort feed (not hunger at this point). I also wanted my evenings back and to be able to put her down awake and walk out the room... We had gotten into a bad habit that was only broken by controlled crying I'm afraid. She would have kept the status quo for ever if I hadn't put a stop to it, she persevered for 2 weeks. It was very hard but totally worth it.
I'm in similar situation as you are in now with my second child who is nearly 5 weeks old... doesn't do more than 2 hours when we initially put her down around 11pm. Then she's awake for 2 hours and we're stuck in a cycle of feeding, napping changing, burping, helping her fart... then she wants a feed again and we're back to square one. Feel like we're going around in circles. If I try to simply put her down after her first wake/feed, she cries, grunts, strains etc and doesn't resettle. We HAVE to burp, wind her etc or it's just worse but this means we're up for ages and ages with her. I also think she has silent reflux, she's very windy, straining constantly (all night). Grunting etc etc... I feel like her sleep is getting worse and she's spending less and less time in the cot. So then started co sleeping with me and even that doesn't seem to be working now. Very unsettled in my bed - whether I feed sitting up or lying down. She takes in loads of air and seems in pain afterwards and needs a lot of help burping. All this meaning she's basically impossible to put down. All this doesn't help you I know but struggling here too and at a loss about what to do. Looking back with my first born, the thought that I just fed her back to sleep and put her down was a total breeze and the least of my worries!
As of today we've bought our first dummy because she is just so unsettled and unhappy - haven't used one before, but really hoping she will take to it. We're desperate. Suspect it won't be easy either. Nothing is. Re the night feeds I do keep her up right on my shoulder for 15mins or so to help with the reflux/burping after the feed, don't know if that makes a difference. I then wait for her to go into deep sleep on me (which can take two three attempts) before finally being able to put her down in the cot or in bed next to me... but only for an hour to an hour and a half before we start all over again.
Good luck, this won't last forever. Try not to dwell too much on the bad nights.
Sorry you're going through this. You're not alone in these sleepless night