I had the same 4L works and 4H does not syndrome on mine. Unfortunately, I was still in warranty so the dealer had to fix it and I only know they said it was electrical--loose connection coming out the tranny (but that was a bozo service writer, not a tech--he could have meant transfer case and probably did).
I don't have your setup--mine is 5sp manual--but I wanted you to know this can happen. I suggest you run the test on the VSV's I described to MDTrailrider in his thread. If that shows the vacuum changes VSV's in 4L and not 4H, then you know the problem IS electrical. I suspect this IS the case because the actuator/VSV setup works in 4L.
Then it is a matter of going to the wiring manual in ncttora and figuring out the engagement loop for the 4H system and focusing on what is different from the 4L loop. That should get you to a solution. Good luck.
I am also pretty sure the screw is not OEM. But we would need to know which hose to hazard a guess as to what is going on.