Mysterious Overheating

Hiya everyone.

1994 Toyota Camry 2.2L, 257k miles
Car overheats
Top radiator hose hot, bottom cold
Very shortly after take off the car begins to climb the temperature ladder
Not a lot of white smoke form tailpipe
Rough idle at first start, fine thereafter
No loss of coolant
No milky oil

What I have replaced/tested:
New thermostat
4 month old radiator
Visibly inspected water pump (went ahead and changed timing belt) no issues, turns freely
Replaced cam and crankshaft seals, no more oil leaks (would have to put in a quart every 70 miles or so. Sometimes sooner and that’s when I realize I have had dangerously low oil while operating the vehicle but I consistently check the level because of the oil leak…I guess sometimes the leak is faster than my checks)
Both radiator hoses show no blockage
Flushed radiator
Replaced engine temperature control sensor
Replaced temperature sender sensor

So with all of this…the temperature still begins to rise when engine is under load. The fans do not kick on, I’m assuming it’s because the fan temperature sensor is not receiving any hot coolant because the lower hose is cold. I disconnected the sensor so now the fans run constantly. I picked up a head gasket leak tester…within a few minutes the blue liquid turned green/yellow BUT I DO NOT SHOW THE CLASSIC SYMPTOMS OF HEAD GASKET PROBLEMS! Not much white smoke (normal for 257k miles), no coolant leakage and no strange noises or power issues. Then I had the idea to take the thermostat out and see what happens. Now the temperature never rises to mid level and the car at least gets me around town when I need to get somewhere. Both radiator hoses are warmish now too. I work from home so it’s not a huge deal plus I plan on ditching the car anyway when I find the “deal.” BUT I have an obsessive personality and I would like to at least solve this conundrum just in case someone else has the same problem and I can offer some sage advice. Obviously I have terrible gas mileage because the engine never heats up. A couple of other strange things. I know I will “burn” coolant but even after the car sits overnight I go to check the radiator cap and I can hear a pssssshhhhhhh and a slight amount of pressure when I take it off. Also, around the time the engine begins to creep to mid level (an indication my coolant/water is evaporating) I can see the overflow tank is completely full or overflowing. I drain that fluid and put back into the radiator then the car is fine for an hour of operation or about 40 miles before I. I can’t see why it would be a faulty cap because of the release of pressure each time it’s opened. I make sure to “burp” the system when adding coolant.

So for my questions:
Is there something I am overlooking?
Why won’t the radiator pull from an overflow tank that is at mid level every morning and overflowing after driving? Especially if the seal/pressure seems to be persistent.
Would Blue Devil or another gasket sealer work for a short period of time?
Is there a blockage I’m not considering?
I know I should have some sort of gasket issues at 257k but is it really the gasket and nothing else?

having to add a quart of oil every 70 miles either means you’ve got a niagara falls sized oil leak, or you’re burning oil like crazy

Besides that, you DO have many of the classic signs of a failed head gasket

If that test fluid turned yellow, you’ve got a problem

Might as well use the blue devil . . . you’ve got nothing to lose at this point

The overflow tank is filling because the head gasket leak is allowing exhaust gas into the cooling system and pressurizing it, forcing coolant into the overflow tank. The residual pressure is what you hear escaping when you remove the radiator cap, and this is what is preventing the overflow coolant from being sucked back in.

It really is just a bad head gasket.