Merc 200 20 hp outboard is possessed, shifting backwards

OK, here's the deal. My 1975 20 hp outboard merc shifts into reverse if I put the shifting handle to the "F" position, which is the forward position of the handle. It shifts into forward if I put the handle to the "R" position, which is the rearward position of the handle. It shifts perfectly fine like that, but it's just backwards and doesn't seem right to me.

I've got the lower unit off and if I turn the shift shaft by hand (or vicegrips), I turn the shaft clockwise to shift from forward-neutral-reverse. If I shift the handle on the engine it works the opposite way! I can look up into the shaft hole with a flashlight I can see that the coupler would turn the shaft counterclockwise if it were to work according to the sticker on the side of the engine cowling.

I've inspected everything I can see, such as the linkage and everything inside the engine housing but everything looks fine. It's almost as if the sticker on the engine housing is wrong, but again the sticker shows that the handle should be pulled to the front of the engine in order to shift into the "F" position, which seems right. And the handle sticks up, so I don't think it's upside down or something like that. I'm thinking maybe there are some mix-matched parts on this thing, possibly in the lower unit. Are some of the lower units interchangable? Should I just put it back together and run it the way it is? What am I missing here?

Any info appreciated. Thanks. Chris.