I agree w/swoop- the first thing to do is a fluid flush. ATF fluid abosrbs moisture & with the unit used so infrequently the absorbed moisture wouldn't have a chance to get hot & evaporate off.

usually harsh enguagement deals with the swash plate (wave spacer plate) in the clutch packs. If it breaks it doesn't cushion the clutch engagement and lets it slam into gear hard. Have seen this on many of them.

but check all your pressures and make sure they are good but you'll probably find it is some hardware problem internally.

And going on what edward said, sitting for long periods of time without use can cause its own set of issues.

try changing the fluid and filter (clean the sump screen) and see if that helps any

Yes, it only has 300 hours on it. The unit belongs to the school district. Actually common for government places to have such low hours. I have had the check all the mounting bolts. They thought resting the pinion lash would fix it. So, I let them do that. It still has the noise and vibration.

really? 300 hours on a truck made over 10 years [and maybe as much as 20 years] ago?
Do you believe it? Because that few hours over that long of a time would cause it's own set of problems.
As far as "harsh engagement of the transmission" the only PSBs for this that I am a ware of, concerned both directions, not only in 1 direction (same parts# used in both directions).
?Have you checked to make sure all the motor mount bolts are tight, and none broken (put a wrench on all the motor mount bracket bolts)?
have you taken pressure readings of the trans?
I am betting you have a broken or damaged clutch disk or clutch housing worn out, or sticking clutch plates (if it really only has 300 hours after 10+ years, then sticking, if worn, then you have lots more than 300 hours...