I had exactly the same issue, my boy is now 4 months too:
Here is our routine:
He sleeps around 9 on our bed and I will transfer him to his cot. I try to catch some eye-shut too and wakes up around 1am to pump (I now pump and bottle feed) and gives him his dream feed when he is sleepy or sleeping.
Around 3-4am when he usually "wakes up" and lets out a whine, I will give a pacifier. Often, he will settle down fast and wake up around 5-6am for next feed.
However, on days that he is so sober and whining non-stop, I will give in and bring him to the bed so all of us can catch some precious sleep.
I will probably invest in bed guards when he can turn over. Heard many stories of babies falling over.
Read more