An impeller new in March should still be in good condition, even if it sat for a while.
To check the resistance of the temp sensor you'd disconnect the wire going to the sensor and connect one meter lead directly to the sensor, the other to ground.
Actually I was wrong about the resistance, this is just a simple switch so it should be open when the temperature is low. The manual I'm looking at says 300 deg F for the switch to close, that seems way high and I doubt is correct. Other motors go off at around 190-200 deg F and that's plenty hot for any 2-stroke. Since your motor doesn't have a thermostat, I'd be really worried if any part of the powerhead was running at more than 140 deg F.
For the alarm module itself, another thought I had is to disconnect the temp sensor only and then run the motor, if the alarm still goes off there's something wrong with the module.
This is the steady tone, right? Which is the overheat; oil injection issues get the 'beep-beep' alarm. And the module does its self-test beeping when you turn the ign on, yes?
If the hi-temp alarm switch is going off at the wrong temp you'll need to replace it if you want to retain that function. Some of these switches are really expensive, others not-so-much. If yours is one of the expensive ones, I'd be more inclined to install a water pressure gauge, which is a more accurate indication of what's going on in the cooling system, anyway.
HTH........ed