both ways are correct.
"There are at least two generations of Reverso cases and carriages - the current ones have a little block on the carriage (only on Grand Reversos?) to prevent the case from dropping down all the way in the carriage while offset left or right.
With all of my old, traditional Reversos, the block was not there, so I slid out horizontally, applying pressure from the side, pivoted, dropped (figuratively, of course) it parallel to the carrier, offset to the other side, then again applying pressure on the offset side, snap it into place.
As you note, this would seem to make more sense, as any wear on the carrier that comes from the spring loaded ball snap will occur on the carrier side, where it is less noticeable, than on the top. And, this was told to me by both long time Reverso collectors as well as JLC staff.
Could it be there are different procedures for Classic Reversos and Grand Reversos?
Do the new standard Reversos also have that carrier block that prevents the case from coming down parallel to the carrier while still offset left or right?"
"The instruction applies specifically to Grande Sport Reverso and Grande Reverso.
For other Reverso case, BOTH ways are considered proper.