I got the same swap that you have, and my car also overheats. I shorted the two wires that turn on the radiator, so they are always on, and the car seems to run fine. It ran good without overheating for a little while, but then things started acting up again. The cars temperature goes up and down. It overheats for about 4 seconds then it starts to go down. It stays at a regular temp, then when I punch the gas petal, the temperature starts to go up again slowly. Do you have the same problem?
Also, what kind of ECU are you running? OBDI P72? The civic cx ecu will work but nothing will engage (like you are describing).
As for the overheating problem, I'm not sure what the problem could be. I am going to replace the thermostat, and hope that something changes, but I am also stuck.