If he is that paniced then I would talk to the vet about medication just during the packing/moving stage and maybe briefly during the readjustment period. It can be so hard on them and expecially with a very nervous kitty.
Another suggestion is that when the time comes to move things out you should put him in a room with some of his favorite and familiar things. Take him and those things in the last trip and set him back up in a room in the new house with all the same stuff. Like his favorite bed, blanket, or toys. Let him have time to adjust to the new smells in that room and slowly introduce him to the rest of the new house. You'll know how fast he can handle it.
Isn't it sad when you know that in the end he will have more room and a fresh air but getting there is so hard. I'm sure he will handle it better than you anticipate but I would try the meds temporarily. Better to be safe than sorry and if it makes it easier on Cubby then it's worth it.
I'm sure you will get lots more advice and great suggestions.

I hope it goes well for you and you get your new house!!