Re the barrels fitting tight to the action flats, actually they should not. The fit there must give some room for the flexing of the action during firing, in gunmaking language the barrel flats should clear the smoke. The tight fit is between the breech ends, the bottom radius of the barrels and the breech face.

From the description, that the play is only vertical and the breech face tight, plus the leftward top lever, it seems that the wear is on the bold bite.