Its running too cold? This is new one for me.
Maybe going up in thermostat temp range would help.
About half on the temp gauge is acceptable for a stock motor i think. Mine is modified and it still never gets over half on the gauge.
I can't see the value in putting a new core into your radiator if its not over heating.
How long in minutes does it take to warm up? Mine takes at least 5-8mins, even after i start driving.
Thermo fans are not designed to run constantly. Most have a lifespan of about 1500hrs at 80 degrees.
I would be going back to the standard fan and trying to source a higher temp thermostat. After all, why would you spend money on a new radiator when installing the standard fan will fix the problem.