The rewire of the relay works great unless something was changed from 09+ ... the problem is the oem circuit breaker between the factory relay and the ecu gets overloaded and cycles, causing the fan not to run consistently, it will over heat just at idle if left alone.
IMO Upgrade the radiator... the main problem is the volume of coolant in the oem system... a larger capacity radiator with more surface area will decrease the time the fan is required to run as well as its frequency between ON time...the OME fan will work fine...there is nothing wrong with a radiator that is too big! that is what the thermostat is for, to keep the engine temp up.
Coming from a guy who has ridden at Glamis when its over 110* out... OEM size radiator is not big enough for a modified 75+ hp motor