TAKE THE CAR TO A GOOD RADIATOR SHOP (ONE THAT SPECIALIZES IN RADIATORS ONLY):
There are too many possible reasons for the car to overheat, so you need a specialist.
REPLACE THE RADIATOR CAP (MOST LIKELY CAUSE OF YOUR PROBLEM):
You wrote that it gushes gallons of antifreeze/water, but where is the leak? An overheated engine is supposed to have enough pressure or temperature to cause the radiator cap to open to spew hot water, steam, and vapor into the reserve tank. If the radiator cap is defective, it will spew when it should not, and this will lower the pressure in the radiator. Maybe this is why you can open the radiator cap without seeing steam and water escaping? The radiator cap is relatively cheap, and it is always a good idea to try the cheap solutions first, especially since you have to change the cap periodically for preventive maintenance.
SOME OTHER POSSIBLE REASONS FOR THE CAR TO OVERHEAT:
1. Bad fan clutch
2. Fan missing blade
3. Air obstructed from hitting radiator (example: plastic bag stuck in front of it), but since the radiator was replaced twice, this is unlikely.
4. Exhaust gas in the coolant water (from a cracked block, cracked head, or blown head gasket). Radiator shops have a special fluid to detect such gas.
5. Timing set wrong. If timing was set by a timing light (light shined on timing marks on the harmonic balancer), and the harmonic balancer separated the outer metal ring from the rubber center ring, the timing marks would not accurately indicate correct engine timing.
6. Clogged exhaust (Kinked exhaust pipe by backing into a curb? Baffles inside muffler collapsed? Banana in tailpipe?)
7. Bad water pump (but you replaced that).
8. Kinked lower radiator hose. The hose is supposed to be rigid, and is often prevented from collapse by springs inside the hose. If those springs rust out, the hose can collapse, causing the water flow to cut off. The lower hose can collapse because the pump sucks water through it. The upper hose is the return line, so not apt to collapse.
9. Water leak. This is why you need to find out where the water is gushing from. Perhaps there is a leaky radiator hose or a soft plug (aka freeze plug) rusted through?
10. Radiator too small (perhaps not enough layers?).