J.S.
Please do not let your baby cry it out this young. His stomach is tiny (think the size of a walnut, so he needs to eat frequently, even at night. It sounds like he is going through a growth spurt. He will eventually sleep for longer intervals, it just takes time. Can you and your husband alternate nights to stay up with baby?
Another suggestion I have for you is to sleep when baby sleeps, so you can catch up on your rest. So, take a nap during the day when your baby goes down, you will feel so much better.
FYI: Most health professionals (including the AAP) do not recommend Babywise. Strict scheduling can lead to failure to thrive in infants.