A '54 through '87 bed is deeper than the '47 though '53 bed. This was possible because the kick up on the later frame isn't as high as on the earlier frame. This is the reason your bed sits too high.
Assuming your bed is pre-'54, which seems likely, you either need to modify the floor of your bed, or find a '47 to '53 bed. I'd look for the right bed.
The apron you refer to is on all the trucks, though yours may not be correct given the bed it is attached to.
