It may feel like a new truck, but that's not likely the cause of a
vibration. The shocks stop the springs from rebounding endlessly after
hitting a bump.

   A vibration has to do with something spinning out of balance.   I'd be
looking very closely at the tires.  Certainly not unheard of for a fairly
new tire to experience a cord seperation.  You might try to find a shop that
can spin them up individually on the car to see if you can isolate one
causing a problem.  There are also driveshaft issues to be considered,
engine vibration at that particular rpm (although you should be able to
replicate the problem in neutral) from an out of balance fan (I've seen them
lose a blade).  Many possibilities, but look for things spinning, not
bouncng.  Sometimes a shock change will reduce or remove a vibration from an
out of balance wheel because it reduces the oscillation, but all you're
doing is covering over the root cause.

You may well be due for shocks at that mileage, but again, they are not the
cause of your sagging rear.  Schocks don't carry weight, the springs do.  If
the back is sagging more than it did it's because the rear springs are weak.
Im not a great fan of compensating for weak springs with an air shock or
spring assist shock if the vehicle wasn't originally equiped that way.  We
used to see kids in the 70's jack up the back of their cars with air shocks,
and would also see a lot of broken shock mounts on the frame or the axle.
If the shock mounts were not built to carry load, just to absorb shock, you
may find yourself in that same boat.

My advise would be to have your rear springs replaced/re-arced and install a
good set of non load carrying shocks.