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All those codes are likely caused by a faulty governor pressure transducer. You don't need to rebuild the transmission for those codes. The transmission temperature sensor is part of the governor pressure transducer. P0711 & p0713 is related to the temp sensor and P1762 is related to governor pressure transducer, so replacing the governor pressure transducer should take care of all the problems. Most people replace the governor pressure solenoid while the pan is off because it has given a lot of trouble. If you decide to replace it, I recommend using a Borg Warner solenoid, they are more reliable than the factory solenoid.
I hope this helps, let me know.
No, I don't think the check valve(torque converter drain back valve) is the problem. It's just a coincidence that it started after replacing the radiator.