this thread got slightly derailed, but I think you got a lot of great advice. I just wanted to add what worked for my family, as we just went through this (my son is 5 months).
He was sleeping in his rock n play in our room from pretty much day one until 4 months old. We kept trying to put him down asleep (same as you, we would rock him/feed him/snuggle until he fell asleep). Then he would wake in the middle of the night and need to be soothed back to sleep. Like another poster mentioned he had these negative sleep associations and would need them to sleep. At my 4 month appointment my pediatrician said that around 4-5 months they might start to catch on that crying= mom or dad comes and that 4 months was the perfect age to sleep train baby. The longer you wait the more the habit will be developed and could potentially be harder to break.
So we did a modified CIO (i’m sure there is a better name for this…) sort of like you described. The first night we started his new bedtime routine (bottle, bath, book, then bed). He got put down awake and happy. Lights out and we left the room. The first night we started with 2 minutes of crying before going in to soothe. I would go in and pick him up/bounce/snuggle/whatever until he settled and stopped crying (but NOT asleep). Then he would go back down awake. After a few days we bumped it to 5 minutes, then 7 minutes, then 10 minutes and 15 minutes is our max (and still is). Once he started falling asleep on his own, he stopped waking at night. We never really had to CIO in the middle of the night, putting himself to sleep solved that for us. If he did wake in the middle of the night we pretty much followed the same routine (leave him to cry for x amount of time, then go in and soother) unless he needed to eat. I can tell the difference now between his I need to something cry and his I’m just being fussy cry. If he starts sounding like he’s getting more worked up, I’ll go in.
Again, this worked wonders for us and was about 1-2 weeks before he was sleeping well. Now at 5 months I put him down, he whines for a minute or two and is out all night.
Like others have said, consistency is key. So whatever you and your spouse decide, make a plan and stick to it for a few days. If after a few days it’s really not working, then maybe try a different method. All kids are unique and it might take some trial and error to find what works.
Oh- also, I really hated hearing him cry (broke my heart), so I would turn the sound off on the monitor (I could still see the little lights go up to know he was crying) and set a timer on my phone for the amount of time we were waiting that night, maybe distract myself with a chore, like doing the dishes. It felt sort of harsh, but it helped me get through it. Sometimes letting baby cry is harder on mom than baby!
Whatever you decide I wish you luck! Sleep training is no joke!