I've been there. It felt like I was reading my own story. I could never let my daughter cry it out so every time she woke, every two hours, for her whole first year, I would get up and nurse her. I justified this because she never nursed for very long, maybe 5-10 minutes, and I wanted her to get as much breast milk as possible. This was especially the case when, like your son, she was eating solids during the day and would not want to relax to breastfeed and refused to drink milk out of a bottle or cup. So, I continued the all night routine till she was a year (my own goal for breastfeeding) then decided it would be worth the pain of breaking this night feeding habit, and basically weening her, in exchange for some much needed sleep.
What I did was slowly drop one feeding at a time by instead giving my daughter her paci and rocking her and rubbing her back until she would finally get to sleep. At first this took up to an hour, which was hard when I knew that just 5 minutes of nursing would do the same, but I thought it better than the alternative of an hour of her screaming. By a week she would sleep 3-4 hours between waking instead of only 2, and it usually took around 15 minutes to rock her back to sleep. Within the month we were down to one feeding a night (from 5) but she was still waking numerous times. And, of course every time she woke she would stand up and be crying for me to pick her up to rock her, so I still wasn't getting the sleep I needed.
One day, in my sleep deprived state, it finally occurred to me that if I didn't want her to automatically stand up every time she woke that I shouldn't be trying to comfort her from above the crib, but instead be down at mattress level. So then, instead of rocking her or leaning over her to rub her back I started sitting on the floor with my head next to her mattress and would not make eye contact until she laid down herself. After only a couple nights she stopped standing up and would roll over to fall back to sleep as soon as she saw me sit down next to the bed. Then about a week later she stopped waking altogether!
I finally realized that to get her to sleep herself, without crying it out, I needed to eliminate the stimulation of nursing, rocking, back rubbing, etc. and just let my presence be enough comfort. Then it didn't take long for her to not even need that. So, now she's sleeping 8 hours, then I do still nurse her once, and she's back to sleep for another 3-4. Unfortunately, I still wake several times during the night and go check on her, I just can't believe she's actually sleeping for so long. I really drew out the process thinking it would be better to slowly change habits than smacking my baby with a new routine cold turkey. So, it has worked but took a lot of patience.
Good luck and hopefully you’ll soon have good nights.