Ford F-150 - 1997-2003 :: Radiator Or Head Gasket Causing Overheat?

The problem is my new-to-me 97 Ford F150 5.4L SOHC engine, auto transmission, is overheating after driving it for a short while. Seems to be fine at idle. I have read previous posts with the exact same issue, but the consistency seems to be all over the map from burping the system, head gasket, thermostat, and possibly a plugged radiator.

Backstory:200,000+ miles.
Truck sat for 6 months after previous owner broke the shift cable.
Truck was in a front end collision. Frame looks bent underneath the engine.

Previous owner had overheating problem. He said he changed the heater core. Looks like brand new coolant in the system so story probably checks out. Desperately needs an oil change. Very black oil.

Previous owner thought the system needed a burping. So I'm largely assuming the problem started after the heater core change, or he misdiagnosed an overheating problem and thought the heater core could cause it. I have found a radiator cap and thermostat in the truck which seems to indicate he tried many things to fix the overheating and was unsuccessful. Engine looks pretty clean for the miles.

Symptoms/Backyard Tests :
Blows cold air with heat on highest level and on defrost.
Blender door fuse intact.
Doesn't overheat at idle.

Ran the truck for 15 mins with the coolant bottle fill cap off on level ground to try to burp it after draining some coolant and checking the thermostat orientation. Coolant level increased in the bottle. Large air bubbles came out. (Another session before this one, I ran it for 30 minutes with no coolant cap, and eventually coolant overflowed the fill bottle. Normal or no?)

Seems to overheat after the thermostat opens. After doing the 15 minute warm up/burp, I took it for a test drive. I drove it about 20 blocks with the temperature gauge on the dash reading the same as the warmed-up idle temperature. Got to the 20th block and the gauge immediately spiked to overheat with the oil pressure dash light coming on. I could be mistaken as the oil pressure light almost looks exactly like the overheat dash light. But I'm pretty sure the temperature icon was on the right side of the oil can icon and not the left.

After the above drive: Upper rad hose too hot to touch.
After the above drive: Lower rad hose medium warm. Could hold on to it if I felt like it.
After the above drive: Upper part of rad pretty hot. Not Insta-burn but hot. Tempature decreases to warm to cool as you go lower down the rad.
After the above drive: Both heater core hoses going to the cab luke warm.
Coolant looks brand new.
Radiator looks slightly bowed. Probably from the accident? Otherwise looks clean and minimal bent fins.
Drained some coolant and pulled the upper rad hose to see if the thermostat was upside down. Looks installed correctly.
No signs of weep hole leaks from the water pump.
Fan seems solid. Has maybe 1-2mm of play in the bearings.
Something that looked like steam from the muffler at startup, that disappeared after getting closer to a normal range warm engine.

I have driven crap cars for many years and I've never seen a plugged radiator which makes me skeptical of it being that. All the radiators I have changed were because they were eventually leaking from cracks in the radiator.

I would also be interested in doing an informal poll if you have read this far and have had this era of F150 that overheated. Have you ever repaired the head gasket? And/or have you ever changed the radiator?