Dave,
No need to stop when shifting in between S and SA. I would recommend to use SA only to get going and the switch on the fly back to S. http://4x4abc.com/jeep101/engage.html
By the way, SA is not AWD - it is part time 4WD. AWD is defined as a system of full time 4WD without low range.
About the vibrations. In S the entire axle assembly and the front driveshaft are rotating without any torque load = little or no vibration. When in SA the transfer case applies torque towards the front drive shaft and any accumulated play in areas where wear has occured over time (transfer case bearings, U-joints, slip joint, diff bearings, wheel bearings, rotor run out) will cause vibrations. Only replacing all parts that can have accumulated wear, including the drive shaft, will get rid of the vibrations.
Also, even slight differences in wheel diameter front to rear will cause tension. And tension combined with a lose/worn out system will cause vibrations.
It is difficult to achieve equal wheel diameters. Mark the center of a front wheel where it hits the ground - drive for 10 revolutions and measure the distance. Then do the same with one of the rear wheels. If distance is longer, reduce rear tire pressure step by step until you get an equal distance. Increase rear pressure when rear distance is shorter.
I had a client some time ago who had front tires of equal nominal size but by different manufacturers and that caused horrible vibrations (in 4WD only)since the two tires had different diameters.
Harald