I think you will find there is no real rhyme or reason or specific method for getting the air out of the system - everything mentioned will work, it just needs to be done over a couple of full warm up and cool down cycles. I had similar issues but after replacing the reservoir and cap with OEM and bled the system over a period of time with full warm up and cool downs it maintained a constant level and the sloshing went away.
One thing that has worked well for me is make sure your coolant reservoir and cap are in good working order, park the truck on a hill, engine facing up hill, heat on full, raise coolant reservoir as high as you can get it, keep cap off until it warms up and you should see some air bubbles burp out. I did this 3 cycles and my sloshing stopped. Another tell tail sign of air in the system is that the coolant level drops significantly overnight with no leaks.
It is true that after a number of cycles and after doing all of the above does not work - your motor is likely being pressurized. Generally that will show itself with a slow drip on the over flow drain. Head gaskets.