Few things here to understand.
When the computer detects high coolant temperature, it will deactivate 4 cylinders to reduce heat and prevent engine damage. Basically, failsafe mode.
Check if the engine is actually overheating when the gauge spikes high. Best to use an infrared thermometer at the thermostat. Also, does the engine knock or make sounds when the oil pressure light is on? You really should use an oil pressure gauge to check the oil pressure. If the coolant temp is normal and the oil pressure is normal, then we are dealing with with some false readings.
If the coolant is indeed overheating and the oil pressure does drop, then that needs to be addressed first. Check for a restricted radiator, water pump impeller broken or rusted, coolant level, sticking thermostat... you know the drill. 14% does kind of worry me. I know that is almost normal but what happens to that reading as the engine is put under a load. As the engine warms up, the head gasket can leak more and cause your problem. You may be dealing with an engine problem if indeed the temperature goes high and the oil pressure drops.
If we are dealing with some false readings, check the alternator for excessive A/C voltage output. Nothing more than 500MV of A/C voltage is acceptable. Best to use a labs cope for this but a volt meter set to A/C voltage will do. Excessive A/C voltage would confuse the computer and give false readings to the computer causing your problems. Quite common for a diode in these alternators to drop and cause this problem.
If the alternator is ok, check all your computer grounds and powers. Yes, use a load to test for grounds such as a headlight with one wire hooked up to power and one hooked up to the ground you are testing. Power testing is just a reverse hookup. Bright light is what you are looking for. Dim light is a problem. A test light is just not good enough I know how hard it is to access the computer but at this point it is a must. If all checks out, the computer would likely be at fault. But, check the wiring harness all the way around for any signs of rubbing through before replacing the computer.
A faulty cluster would not cause your rough run since the signals go to the computer first, then to the cluster. A faulty cluster will show bad readings but not make your engine run rough.
I stand firm with my first answer.If the coolant temp is in fact at normal range and the gauge says otherwise, then there is a sensor problem. Since you have new sensors, I doubt they are the problem. But, I have seen wrong parts or bad parts. So, new never means good. you need to check your alternator A/C voltage output before going any further.
If that is good, check the coolant temp sensor wires for having an intermittent short to ground. Make sure that the sensor ground wires do intact have a good ground.
Test the computer power and grounds.
But, did have an afterthought.
When the problem is occurring and the fault is in the instrument cluster, I could see how a faulty cluster can bring all kinds of voltage feedback into the engine computer sensor readings. When this happens, unplug the instrument cluster and retest your readings and engine running quality. If all cleans up, then a cluster is your fault. Have never seen a cluster actually put the computer into limp mode due to cylinder head over temp, but I see how it could be possible.
Now, a silly question. You did install the thermostat in the correct way. Spring into the engine? You did install the correct sensor into the correct place? I think those plugs can go into both sensors.
Check that the sensors have a good ground and that the neither of the signal wires are shorted to ground.