Chuck is doing much better! He's eating and pooping normally. We have been home more the past 2 days and took a break from packing and he seems to be more comfortable.
I'm going to try playing with him while packing, like playing with the packing paper, talking to him while I pack, etc. Maybe that will calm his nerves.
In a couple weeks when we get the keys, we're going to take him to the new house so he can sniff around and get familiar with it. Thanks everyone for your advice