As others say, who have paraphrased the carburetor guys that frequently contribute on this site: It's never the transmission, always the clutch (except when its the transmission)
Seriously, this does sound more like a clutch issue. As klhansen mentions above, the input shaft is still turning when you try to engage first gear which is why you hear grinding. And as you observed, when you are underway, the relative speed of the gears is closer, so they engage more easily.
Also, while the clutch was replaced, was it the correct one for this application - or just the same one that came out of the truck? The two might not be the same. What was the condition of the input shaft ? Any weird looking wear patterns on the splines or pilot bearing contact area? Could there possibly be an alignment issue between the engine and the transmission that is causing the clutch to hang up?
Maybe you could drop the inspection cover and with the engine off, and look up in there while someone operates the clutch. You should be able to see the plate inside the pressure plate assembly retract away from the driven disc.
BTW, Is this a diaphragm type pressure plate? Not sure about the ones specifically used on your truck, but in general, the diaphragm spring in some can be bent if the clutch linkage is adjusted to provide too much over travel.
Best Regards...
