Actually OUT of gear if it's a MerC Alpha I/O...
If it's any MerC I/O then:
Two cables out of the helm control as noted above. One throttle to the carb or throttle body. Other to a Shift Plate where that Interrupt Switch would be. In MerC terms, it's the Upper Shift Cable.
Then a third cable from the Shift Plate down to the outdrive itself.
Troubleshooting stiffness would be to disconnect Upper from Shift Plate. Throttle should do all funtions effortlessly, Throttle Only button pressed or not. If that test fails, and it was OK with the button pressed, then Upper Shift Cable sticky --OR-- problem in Helm Control. If effortless either way, disconnect Lower Shift Cable from Shift Plate and try to shift by push/pulling on the Lower Shift Cable. Should have assistant rotating the prop so it'll fall into gear when it needs to.
Problem I see here is if it's as stiff as stated, I think the Interrupt Switch would kill the engine going into or out of gear. As I said, should only operate coming OUT of gear. And only with a prop installed and in the water. All it does is see if the force needed to shift gears exceeds the tension of a Forward and a Reverse spring on the Shift Plate. That should only happen coming OUT of gear IN water. That's when torque against the gear engagement is so great that the operator couldn't pull it out of gear. The Interrupt Switch causes a miss at that point to lower the torque. If the shift mechanism is sticky from Shift Plate on down, 95% of the time Lower Shift Cable, then the Interrupt will work when it doesn't need to and the engine will quit or not start.