I have a similar problem, only different.
I have a 203 case (with part time kit) and I have to always either A) drive with the hubs locked or B) drive with hubs unlocked, in 4wheel.. In other words the Front driveshaft has to be spinning the same rpm as the rear, or it creates a really bad knock. With the front hubs locked, if I peel out on dirt or something, it still does it because they are turning diff speeds.. It sounds sort of like a gear barely engaging, trying to grab.
Is that at all similar to your problem? I know we have totally different transfer cases but its worth a shot.
Im a little confused as to what you mean by Transfer case in NEUTRAL and Takes off.