Couple of questions, thoughts:
On the new radiator, was it truly new or rebuilt? Did the rebuild include upgrades like an extra coil?
Have you replaced the fan clutch?
Have you considered replacing the fan with one that has more blades (plastic, not metal)?
Bypassing the heater core will make overheating worse as, when the water flows through the heater core, it acts like a supplemental radiator.
If all else fails, consider aftermarket electric fans. It's a tight fit but can be added.
I have a similar issue with the engine miss and stalling. Hope someone can post a few ideas on that fix.