I'm afraid that, if I feed him after 45 minutes of crying, he'll just learn to cry for 45 minutes SO THAT he can eat.
Hi hun, no in the middle of the night you'll only feed when they are hungry. You don't want to start a prop for sure.
But honestly if you are moving then I would just wait until you move and he is feeling better and work on gradual withdrawal from there. My lo never took to pupd and would just scream and scream. It works for many lo's but certainly not all.
Here is the info for gradual withdrawal
The Gradual Withdrawal Method
The key to Gradual Withdrawal is to take tiny steps and make the changes very small at first so the child barely notices them. Create a plan, broken into small steps of how you will reduce the parental dependence and work towards independence. For example, patting on the back becomes lighter and lighter until the hand barely brushes the child's back, but is poised just above it.
To implement, follow your bedtime routine being certain that your child has sufficiently wound down from the day. When wind down is completed, lay your child down, tuck them in and use a phrase they can associate with it's sleep time such as "time to go night-night you can find your blankie/pacifier/suck your thumb/etc. to help you fall asleep." Settle your child in their crib/bed and comfort as you normally would, then implement the first step in your plan. Depending upon your child's temperament, you may be able to tackle more in less nights, or need to do less over the course of more nights.
The Gradual Withdrawal Method is intended for children that are reliant upon a parent's presence to calm them and help them settle for sleep. Examples are: sitting in the room, holding a child's hand, laying down with a child, patting to sleep, among others. The idea is to simply reduce the reliance on parental presence gradually and in very small increments so the child continues to settle well and gains confidence in their ability to fall asleep independently. The parent is there to assist the child in sleeping, but slowly reduces the dependence. Examples might be: moving a chair closer and closer to the door until out of the room over the course of a few weeks, moving out a child's bed to an air mattress on the floor, then slowly move farther and farther towards the door over time, reducing the length of time patting though still staying with the child - then slowly working closer and closer towards the door.