Job once asked a rhetorical question, "If a man dies, shall he live again?" (Job 14:14). The answer to that question is "No." "And as it is appointed for men to die once, but after this the judgment" (Hebrews 9:27). Therefore, we start with a fundamental truth, in general people only die once. There have been a few exceptions when God raised a few people from the dead, but that is why what happened is called a miracle. This isn't the way the universe works. People die and don't return to life.
Then what about these reports of people who died and then brought back to life? The obvious conclusion is that the people were not as dead as those around them supposed. That they were near death would be a given, but using the Bible as a guide, we would not conclude that they actually had died.
What about the things reported in near-death experiences? Many doctors have noted that reports of near-death experiences are very similar to how patents report feeling while under anesthesia ["Correspondence," pages 5-6]. If we add in the fact that all of us experience strange things while unconscious in sleep -- sometimes feeling very real when we awake, then we can't rule out that these experiences are not actual experiences of life after death.
As you noted, the reported near-death experiences are almost universally positive, which runs counter to what Jesus stated in Matthew 7:13-14. Near-death experiences are not reflective of what the Bible says happens after death.
One correction is that you assume that judgment takes place immediately after death. The Bible does not teach this. It says that judgment is the next event after death, but Hebrews 9:27 doesn't say if there is a gap between the two events or not. Neither does "For we must all appear before the judgment seat of Christ, that each one may receive the things done in the body, according to what he has done, whether good or bad" (II Corinthians 5:10) state when the judgment takes place. Other passages tell us that judgment won't take place until Jesus' return. "Do not marvel at this; for the hour is coming in which all who are in the graves will hear His voice and come forth--those who have done good, to the resurrection of life, and those who have done evil, to the resurrection of condemnation" (John 5:27-28). "Behold, I tell you a mystery: We shall not all sleep, but we shall all be changed -- in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed" (I Corinthians 15:51-52).