Nighttime sleep

I will preface this by saying my son is my second and I definitely know newborns need to wake a lot at night to eat. Since birth he's really only woken twice a night and we were able to stop waking him to feed early on. For the last few weeks we've been able to get him on somewhat of a bedtime routine with our daughter who is 2.5 and both kids are in bed by 7:30/8:00 p.m. I will then do a dream feed around 10:00 when we go to bed because he usually gives us a 5-hour stretch. What we've been finding lately is even when I feed him between 2:00 and 2:30 (depending on when he wakes up) he's then waking up an 1.5 hour later around 4 a.m. he doesn't seem to be hungry and will take his pacifier and go back to sleep but then he'll wake up again at 5:00/5:30 which is when we usually feed him because it's been 3 hours at that point (and he's refusing the binky so we know he's hungry). Then he dozes on and off but usually wakes between 6 &6:30 We were playing the pacifier game to get him to stay asleep until 7:00 but we've finally just given up and started getting him up at 6:30 or whenever he wakes up after 6:00 in the last couple of days. My question is should we just feed him when he wakes up at 4:00 a.m. knowing he'll just eat a small amount and possibly be up an hour later or do we keep trying to get him to settle and hope that in the next few weeks he can do a second longer stretch so we're skipping the 4:00 a.m. wake up completely?