The engine turns the same way forward or reverse, the gearbox in the leg does the forward or reverse bit. As far as I am aware the gearchange needs the leg in water to work.
It's a pretty fine adjustment on the leg gear cable (engine end) between engaging and not, sometimes even half a turn can make a difference.
Have you had any work done to the gear cable junction area (bolted to the inside of the starboard exhaust risor) where the shift interrupter switch is located?
Sounds like you could be due for a new shift cable, the short one from the engine to the drive. The shift interrupter switch should only work when going back into neutral, get someone to shift while looking at the microswitch if it moves while going into gear then the cable has too much friction and needs changing.
Just make sure its adjusted correctly first as if it has too much throw one way it can operate the switch before its got to then end of its travel, but usually if that happens then you don't get enough travel for the opposite gear selection to work and it makes that horrible hacking sound as the gears bounce over each other in the drive.