How sloppy is the shifter? it maybe time to upgrade. It could still be a syncro/tranny trouble, if it will go in as soon as you stop but wont go in after idling in neutral its syncros not adjustment, as John said finding the reverse gate should clarify. The syncro actually works as a brake to allow the shafts and gears to coordinate their speed for a clean shift. In neutral the trans naturally rolls over internally due to the rolling resistence from to the input shaft and custer gear which are constantly spinning with the clutch out. Once "gear roll over" has occurred the shafts and gears must coordinate their speeds to allow the syncro hub to slide over the syncros and the gear teeth (look at a picture of one, main gear teeth and then syncro mesh teeth on a gear). The brass syncro or blocking ring works as a cone style brake to slow the movements or catch one up. If when if was built even fresh the builder didn't scruff or score the meshing cones they will work like glazed brake pads and therefore requiring more force to stop the other surface.

I know it was long but hopefully it makes sense. What do you think John, is gear roll over the possible cause? Secondly, can you drill the hole in the reverse lever or is it not in the 1/2 3/4 either?