Assuming you have an all original drivetrain in your Suburban, my guess is that you are simply experiencing normal driveline binding that occurs when you engage the 4x4.
I guess my question should be....Are you expecting it to disengage immediately?
The NP208 can, and will have a delay in 4x4 disengagement due to the fact that the linkage is set up so that you can put the transfer case back into 2wd without having to force it like the older NP205, and NP203 required you to do.
Try putting the t-case in 2WD and driving forward in a straight line for a few feet. If your 4x4 doesn't disengage after a little while you may have a weak disengagement spring.
There is a little coil spring on the shift linkage that pushes the 4x4 shift fork into disengagement when you deselect 4x4. If this spring has weakend over time, or the shift fork, and rail have become dirty, or gummed up, this could be the cause of your problems.
Part number 32 in this exploded drawing:
