I need help here and I am wishfully hoping the experts here would be able to give me something to look for with the issue in my G35X (miles: 131800). So, of course, my car is overheating, and I cannot for the life of me figure out what or where the problem is.

Background (and changes made based on suggestions from this forum):
- Thermostat changed with OEM thermostat from Nissan
- Flushed and burped system with Lisle Anti-spill Funnel for almost 30 minutes
- Upper and lower radiator hoses feel the same temperature (within perception error)
- Heater works - hot air blows (guessing water pump is fine then)
- FCM changed recently (due to a blown cap, replaced with Gates FCM)
- A/C works fine and forces both fans on when turned on
- Refilled refrigerant (wasn't necessary, was almost full on Freon)
- Radiator fins look clean and straight (except for just the top row with some bent ones, which is about ~2% of the entire rad area)
- Relays tested both in and out of circuit (voltages checked using multi-meter and conform to Infiniti specs, relays work)
- Checked for blown head gasket symptoms, no coolant smell from exhaust, engine oil is still clean yellow (not gooey) and coolant level hasn't changed

Here's the latest issue:
The ambient was about 82°F here in Virginia that day. I was idling in the parking lot to let the engine get to optimal temperature (with the OBDII scanner connected to read the temps). I started driving when the temperature reached ~182°F (179.20°F is the thermostat opening temperature). The A/C was on and the fans could be heard running at good speed (I used a Kroger bill to test and it would stick to the front grill due to the suction power of the fans). I drove for about 10 minutes and reached the parking lot. The temperature was reading 183.20°F at this point. I kept the ignition on and was idling, and the temperature stayed stable for about 15 minutes with the A/C on, only rising to 185.20°F. Now, I decided to turn off the A/C and see what happens.

The fans turned off in a while and the temperature started creeping up slowly. The fans came on at low speed at 208.60°F, at 213.80°F the fans started at high speed and the temperature backed down to 203°F. Normal behavior, right? Here's the catch. The temperature again started rising (as is usual during idling), but this time, the fans instead of going full blast beyond 213.80°F, started doing an oscillating motion, and making a pattern that closely resembles a sine wave of speed, going between low and high. This has been the story for every time the car has been overheating, the fans do this oscillatory motion and I am not sure why. I turned on the A/C at this point to force the fans stay on at full speed, but that seems to do nothing. The fans just keep doing the oscillatory motion and the temperature keeps going up. I turned off the ignition at 225°F (that's hot).

Note: If I let the car cool and start it again, the fans work just fine until you repeat the above cycle and the fans end up doing the same oscillatory thing.
P.S.: Not sure if this is related, I have been getting ~12 mpg in city.

Any help from this forum would be greatly appreciated. Please let me know if you need more information and if this makes any sense. Thank you so much in advance.

Only thing I can think of, is the fan control module. This is the square black box with what appears to be metal studs facing forward and is mounted behind the driver's side fan. I have no idea on how you can check it to make sure it is working properly. They are under $40 on Rock Auto.

Sounds like the fan motors themselves, the relay is not going to cause an oscillation that would be a bad fan motor.

Probably what's happening is the fan motors work FOR A WHILE then the motors themselves are becoming heat soaked and no longer spinning properly.

Thank you for the suggestion! I did indeed replace it recently, having had a blown capacitor in the Fan Control Module (FCM). I replaced the previous with the one by Gates from RockAuto recommended for this car. My car is still having the heating problem.
Does anything else come to your mind? I am totally clueless at this point.

Thank you so much for taking the time to help.
This, this could be a thing. Do you recommend changing the fan motors? Are they easy to get to replace?
Also, do you recommend RockAuto? Or should I get them from Infinitideals or someone alike?

The fan motors are a fairly common item to fail, rockauto will be fine.