Take the thermostat out of the car and see if the problem persists. As was mentioned earlier, installing the thermostat backwards or if there is an interference with its opening due to its design, it could also be faulty. Taking it out removes it from problem statement.
Thermostat should say "Engine Side" on it and should have a weep hole in the plate body, hole should be orientated in the top position when installed. Drill on 1/8" hole if it does not have one.
If this is an option for your engine: Get a "Balanced Thermostat" designed thermostat. I believe they fail open.
If your fan temp switch is similar in design and operation to a SPF. (two wires in a plug on the radiator) just remove and attach the two wires together or jump them (they are just a ground switch) If you have a single wire sensor in a hose or radiator, it is also just a ground. Just disconnect and use a jumper wire to a new ground to activate fans. Don't know if your fans will run with ignition off. SPF's will. Take one component out of the equation to get fans running. Another thing to verify is direction the fan or fans move the air. Air should be moving "into" engine compartment.
If you have original style Smiths gauges with a gas bulb temp sensor, and if the bulb sensor in mounted on the top of the intake manifold, when filling the cooling system and running the car (cap off) you can loosen the fitting for the bulb temp sensor on the manifold to let air escape. when the air escapes and
antifreeze starts to seep out, tighten it back up. Front wheels elevated helps air to pool and escape. Even just a sloped driveway is enough angle. May take a few heating cooling cycles with cap off to remove all air in system. I note in photo you do not have a catch tank installed. Are you loosing
antifreeze from small pressure relief hose when overheating? Both big hoses get hot right when you were having problems. When system is running correctly the new expansion tank should only have fluid in it up to the divider plate inside. Put you finger thru the radiator cap opening to feel the divider plate with large hole in it. The rest of the tank is for air and liquid expansion.
Hope this helps,
Blas