I can answer your question. The gearcases differ in the way load bearing bearings and gears are placed in the lower unit. In a standard rotation engine, the bearing and gear at the front of the gearcase (the part opposite of the prop, you know the bullet looking end) always have the forward gear. In a counter rotation gearcase the forward gear is always at the back. You cannot change the shift lever of a standard rotation gearcase to make it counter rotating, it will destroy the gearcase. You would be putting all of the load on the reverse gear and it's bearing, which are not designed for that use. Hondas counter rotation gearcases come apart the same way, unlike other brands of gearcases, however, the difference is in the bearing carrier which is different in the gearcases to handle different types of bearings.
I work at a marine engine and gearcase rebuilder. We supply shops all around the country. We build thousands of gearcases. I am also a certified Honda marine tech. Please do not try to change your standard rotation gearcase into a counter rotating gearcase by switching around cables or shift rods. It will destroy it.