Remember that the Genuine HD Electrical Service manual was written for Service techs at Dealerships and it was not written for weekend warriors like myself (or us). Therefore the steps in the manual can at times be blunt, nasty and expensive. This is the case in your situation.
If you follow the flow chart for a DTC P0374 in the Electrical service manual it now says to replace the ECM. Remember, they think your a HD tech in a dealership with tons of parts at your fingertips. Flowcharts are not written to trap and solve 100% of the problems 100% of the time. If following a flowchart fixes 90% of the problems, 90% of the time, they are considered to be well written flowcharts. That is the industry standard.
So to re-cap,,,
1) You have Replaced the crank trigger sensor with a NEW GENUINE HD crank sensor.
2) You have measured a SOLID 3 VOLTS AC across the crank-sensor while cranking.
3) You have check the Crank-sensor connector to the wiring harness and it is clean and tight.
4) You have NO other codes other than P0374. No other codes have appeared. P0374 was your starting code and it reappears quickly after it has been cleared.
5) The Bike starts cold and runs OK for a minute at which time it starts to break up,,, the check engine light comes on (current code logged) and when the error log is checked, you find a P0374 DTC.
6) ***Have you made any changes to the wiring harness? Have you added any accessories or cut & tapped into the wiring harness? Have you changed your plug wires or coil to something other than original stock? Have you unbundled or disrupted the wiring harness in any way? Are you running the original factory ECM? Did you make/add/or change anything electrical around the time you found this P0374 error.***
You have to keep in mind a few things. When the service manual says to check the output voltage of the crank sensor, they are using a break out box and you did not. That can make a big difference since you are removing the electrical load (the ECM) on the sensor.
If you want to give up trying to fix it yourself, now is the time to take it into a shop. If you don't want to take it into a shop, answer Each of the above questions and I will give you some additional steps you can take in order to probe a little deeper.