Three of six injectors are bad. And the remaining three aren't even all the same type. Could this be the cause of my overheating engine?

It is possible that the failure of the three cylinders to operate properly could cause overheating issues. I would however check for bad head gaskets, as well as a blocked radiator, missing air diverter under the front of the car, low coolant, bad thermostat, air in the system, bad hoses of a host of other possibilities.