I hear ya, I'm not too comfortable wrenching on it either. I think Mr. Leary was trying to say that sometimes you need to be quick and powerful with the shifting (in his words, "a little more of a tug"). I've already experimented with different levels of pulling strength, at varying speeds, on a variety of surfaces, etc. It's that magical 30 MPH that I can't exceed when I want to shift into 4-Hi. My mechanic changed out the fluid in all the drivetrain boxes, so I guess the next step is to have him open it up on the bench. I decided to pose the question to the forum first, to see if anyone else had the same problem and possibly a less expensive solution...
Sorry if I was a little vague. thelizzardking is correct. To clarify, do not yank on it with both hands, nor should you kick, punch, or speak meanly to it!

I have just found that with mine, it takes a little more persuasion when you are moving than it does when you are not (i.e. neutral vs under stress in drive). If you are pulling the lever slowly, it will bounce off because it is not catching. When I took one apart a while back, there was not a clear "place" for it to catch the chain. It should be able to engage anywhere in its rotation, hence shift otf, because the whole assembly catches, not just one part.
There should be nothing magical about 30mph. There
is something magical about 50mph or so... don't shift into 4hi when you are driving fast for risk of damage to the drivetrain (as per the owner's manual).
Inspect for leaks. As always, unlubricated parts can cause big problems.
Make sure you can engage the transfer case in all positions while in neutral. While driving slowly try 4hi (not 4lo), and then try it again with a faster flick at speed. The fact that you are hearing the grinding noise means that it is trying to engage.
Personally, I try not to shift while moving when it is avoidable, partly because of the uncomfortable noise it can make if it doesn't engage. I don't think what you are experiencing is anything new. Mine has done the same thing, and my transfer case still shows few signs of wear at 186k on the ticker.