Engine overheats while ilding?

Also, I have the vehicle on a slight incline, so the vehicle is going upward while burping.

I didn't notice the jet engine noise. I had a box fan on top of the motor helping to cool the motor the 2nd time trying to burp the coolant. But I thought I had it burped, so I left and got up to about 35 mph for about 50 yards and then the temps started climbing from 205 to 217. So, I had to turn around down aways further and I was putting it and it held steady and went up some more to 221. So, I turned around and picked up the pace a little and it started to come back to 205 to 208 degrees. So, I repeated the burping and noticed no movement in the coolant with the cap off at the top where the cap goes so, I put the cap back on. It wants to overheat cap on or off at idle. If I hold it at 2000 RPMs constant it will come down to 199 to 205 and not climbed, but I let off and in 20 seconds temperatures start to go back up. It had pressure because I unscrewed the cap while it was still hot in a hurry. And it wants to spew so I know there is pressure.
It's just weird cause it was fine before I hosed out the heater core hoses and let about a gallon of fluid come out the block where the two hoses connect. Radiator feels symmetrical hot when I run my hands up the sides and down on both ends like no cold spots.
With truck off and give the fan a spin by hand it spins a third revolution maybe half.

I had the hood open all the time other than driving.

When is the little fan supposed to kick on over by the battery tray? I turned the A/C on and it came on, but it didn't help from overheating at idle.

The heater seems to be working better. I flush the heater core every year or two because when I bought the truck it was doing the blow the cold air on drivers side. So I use the the garden hose to blow it out. Seems to have helped getting hotter air on drivers side.
So you think it's the fan clutch? Truck was holding temperature fine before I cleaned out the heater core. Do you think the box fan blowing could affect the fans ability to cool the motor? But it still heated up going down the road with light throttle and I didn't have the box fan, so unsure.

I did have the heater on when I was burping the coolant with the cap off and back on. It took a while to get the thermostat to open. The truck started to want to overheat with the cap off and the thermostat was not open yet. So, I was pumping the upper radiator hose and giving it throttle to 2000 RPMs and it just finally opened. But it still wants to overheat at idle even after it finally opening. I flushed the radiator, and it seemed to have flow out the drain when I sprayed the garden hose down the top at the radiator cap. Have a fan clutch ordered to install. The thermostat I replaced a few years ago. I don't drive the truck a lot. So maybe 5000 miles driven in the last 3 years.

I have still been working on this issue. I replaced the fan clutch and a new 203* murray thermostat at the same time. Still having same issue. I bought a coolant funnel kit where you can burp the radiator coolant while running. I did that the other day for 35 to 40 minutes. I was getting bubbles when I rev the motor and let off. I stopped after 35 to 40 minutes cause I didn't see any more builbbles and the temp was holding steady.
Took the vehicle out and drove it 5 miles seemed fine and parked idled for 5 to 10 minutes and still fine.
Go out to check the truck again after setting for 3 days. Let it idle to 170* and give steady rpm for 1 minute to get it more up to temperature. Got it to 192* and let it idle the rest of the way. Slowly starts coming up and thinking it would stop at 203* it just keeps climing up to 214* so I give it throttle to 2500rpm steady and takes 15-20 seconds and starts coming back down to 199*- 201*. Let it idle again and stays around 205*-207*. Hook up vaccumm gauge to get readings and it has steady 19 psi at idle. Steady 2500rpm it goes to 22.5 psi let off throttle and it bumps to 25 steady and back to 19 at idle. I do quick revs and let off a few times and vaccum drops to 11 psi and then back to 19 psi at idle.
So I took it out on a 12 mile dive and it does okay. With temps go to 208* and then back to 203* it does that on and off driving. Sometimes staying at 203*. Get back and park it at idle for 10 minutes and stays at 205* for 5 minutes and then to 203* for 5 minutes before I shut it off.
Sp it this point I don't understand why on cold start all the way to warm mostly at idle the motor wants to overheat and just keep climbing the coolant temps but I rev or drive it and idle it after it's fine? Not sure why it's doing that? I don't want it to overheat sometime out of no where driving or at a red light even though it's been fine idling after driving.
Sorry for the long post.

Here is a clip with steady 2500rpm and then rev the throttle. Seems to be okay

It's 203 degree thermostat. It was the same as the one I had in it before. I thought while I had the coolant out I would replace the thermostat.

I did some more testing today. I first took the truck out on a drive from First starting it up and the temperature kept climbing up to 214 degrees and I thought it was going to keep going but it stayed there for about 10 seconds and then started to come back down to 200 degrees for a minute and then to 203 degrees the rest of the 25 minute drive other than accelerating it would get to 208 and back to 203. When I got back I did the combustion leak test in the resivor because I couldn't get the fluid low enough in the radiator and the blue liquid never turned yellow. So unsure why on cold starts it wants to climb the temps like it's going to overheat. Unless it's air in the coolant don't know cause I burped it with the funnel for 30 minutes last time. Not sure exactly what's causing it.