I tried to nurse no more than 2 times in the night, usually around the times I would have previous to the madness, so around the time of the DF 10-11pm and then early morning, no earlier than 4am. Other times I would just pat/shush or DH would walk him around a bit and hold him until he drifted off. I didn't want him to get in the habit of consuming all those calories in the night by feeding him back to sleep. Like your DD, he eats way better at night. Daytime feeds were horrible at 3 months because he wasn't hungry enough and he's so distracted by the slightest thing.
Transitioning to the 4hr was really hard during this period because DS because became so chronically OT from the bad nights that every nap became 30 mins. So, my rule was I would get him back to sleep after every 30 min nap, even if it took another 30 mins to do it. I would usually give him the pacifier and see if he would be willing to go back to sleep. If he keeps crying, I would pick him up quickly before he fully awakens or it's game over. Sometimes he would drift right back to sleep and I'd get another 45 mins out of him.
Anyway, I would suggest starting with keeping the feed times at 3.25 or 3.5hrs, so it's more of a EASAE pattern. Keep the activity really low-key before the feed. Start trying to stretch the A times. If your DD is the type to get OT easily, do it only in 5 or 10 min increments every few days. At 3 months, 1.5hrs is average, so I wouldn't push it too much. They just naturally start being able to stay awake longer and even nap longer if you get the A time right. What will eventually happen is you won't have enough time in the day to do the catnap so you will be forced to drop one nap. The days are wonky for a bit when that happens but eventually it evens out as they start staying awake longer.
The weird thing is that I was so anxious with both kids to get them transitioned and really in the end they did it naturally in their own time. DD wasn't able to stay awake 2 hrs until almost 5 months while DS is already capable of it and he's just turning 4 months. Just be patient and don't get too crazed because each day is a bit unpredictable for a while.