Pull the hand guards, and then punch out the gas tube roll pin in the sight tower. The gas tube may be a bitch to get out of the tower if the upper has been shot a lot, but the tube should pull straight forwards towards the receiver, then twist it and pull it back past the sight tower (carrier out of the rifle).
Put the upper in an upper vise block, then put the barrel wench on the barrel nut and turn counter-clockwise. Once the nut is spun all the way free, pull the barrel straight out without twisting. The barrel extension has a pin on top that mate to the upper receiver barrel socket slot.
The barrel extension is installed at 175lbs to the barrel, so don't even thing about trying to remove it from the barrel. If you did remove it, then you would need to re-index the extension with the front sight tower.
The areas to check are the barrel to make sure it's straight, the lip of the barrel extension socket on the upper receiver to make sure that it is square and lip bur free, then the mating surface inside the barrel nut to make sure that it is not packed with crap. Don't try to remove the delta ring; you would have to remove the front sight tower to get it off the barrel any way.
As for re-installing the barrel, lube the threads, then tighten the nut to 35lbs, then loosen and retighten for three times. On the third time, hit the 35 lbs mark, then check the nut spine to see if the gas tube will pass threw. If the nut spine is blocking the tube, tighten the barrel nut more, but do not exceed 80lbs.
A sight index bar works great to get the front sight tower in the correct index position, but if you don't have one, a piece of string will work to get the tower close to the correct index. Just run it threw the rear sight centered, and tie it off on the front sight. When the sight tower is in the correct index position, the string should be centered in the carry handle (your just going for close to correct index, the final index is determined by live fire).
Also, unless you want to loosen the barrel nut another time to re-index the sight tower for fine-tuning, the leather mallet trick will drift the entire barrel in the upper receiver socket at the range to get the sight indexed/zeroed. just remember to only hold the receiver when you love tap the front sight tower. This will transfer all the impact energy to slipping the barrel in the upper receiver, and not mashing the tower pins against the tower and just drifting the tower on the barrel.
Hope this helps.
P.S. I type at around 70 words a minute and the rifle is second nature to me, I have been shooting them since 1968. Although it may appear that I have spent a great deal of time regarding your post, your problem is just the same old thing that has occurred here may times here at AR15.com. If I want to get real lazy, I could have just re-directed you to some of the old posts on the subject.
Also, get/reload some real ammo. With the UMC ammo, you will be lucky to even keep the shots on the paper at the 600 meter mark.