I'm one of Jehovah's Witnesses. We don't use the term "soul sleep," but we do believe that a person (or "soul") ceases to exist when they die, meaning that they return to the dust (Genesis 3:19), and they have no consciousness or ability to communicate with the living. (Ecclesiastes 9:10) Sleep is a good analogy (and it was used by Jesus himself concerning Lazarus at John 11:11-14) because it implies that they are in a state of suspended animation, and they can be "woken up" by being resurrected, as Jesus did for Lazarus. This could be a heavenly resurrection with a spirit body or an earthly resurrection with a fleshly body.
I won't directly address those testimonies of Catholics and others who claim to have communicated with the dead, but the Bible itself contains one such story of someone allegedly communicating with a dead person, and I'll address that one. The story is at 1 Samuel chapter 28.
For some context, the Law from Moses specifically forbade trying to inquire of the dead, and it prohibited consulting a spirit medium. (Deuteronomy 18:10-12) Leviticus 20:6 even calls such an act "spiritual prostitution." It was a common practice of the surrounding nations to try to consult the dead.
At that time in 1 Samuel 28, the Israelite King Saul had become alienated from God. Unsure of what to do in the war against the Philistines (verses 4-6), Saul went to a woman who was a spirit medium in the city of Endor (verse 7), and he requested to speak with the prophet Samuel (verse 11), who had died some time ago (verse 3). The spirit medium then claimed that she could see Samuel, and she related what Samuel had to say to Saul (verses 12-19). This resulted in a damning judgment message against Saul.
An article published by Jehovah's Witnesses in the Watchtower of January 1st, 2010, comes to this conclusion:
Think about it. The Bible states that at death a person “goes back to his ground” and that “his thoughts do perish.” (Psalm 146:4) Both Saul and Samuel knew that God condemned contact with spirit mediums. Why, Saul had earlier taken the lead in ridding the land of spiritistic practices!—Leviticus 19:31.
Reason on the matter. If faithful Samuel were still alive as a spirit, would he violate God’s law and cooperate with a spirit medium in order to meet Saul? Jehovah had refused to talk with Saul. Could a medium, in effect, force God Almighty to communicate with Saul by means of dead Samuel? No. Clearly, this “Samuel” was not God’s faithful prophet in any form. It was a spirit—a wicked demon pretending to be dead Samuel.
Demons are angels who rebelled against God’s authority early in man’s history. (Genesis 6:1-4; Jude 6) These demons can observe people while they are alive; they know how each one talked, looked, and acted. They are eager to promote the idea that what the Bible says is untrue. No wonder the Bible warns against having any contact with such spirit forces! (Deuteronomy 18:10-12) These wicked spirits are still active today.
Now we may see why many tell of “hearing” or “seeing” dead loved ones. Though such apparitions at times may seem friendly, wicked spirit forces are out to deceive humans. (Ephesians 6:12) Also, think about this: Jehovah is a loving God who cares for us. If the dead were alive somewhere and they could come to the aid of their friends and family, would our loving Creator forbid such contact and refer to it as “detestable”? Surely not! (1 Peter 5:7) Is there, then, any reliable source of help?
Considering that God prohibits the living from speaking with the dead, it would be natural to conclude that God is trying to protect people from something bad. God and his faithful servants would never violate God's stated law, so we can conclude that all such occurrences of the dead are actually intelligent demons who are deceiving ones into thinking that God's Word is wrong and that humans actually do continue to live on as conscious spirits.
Jehovah's Witnesses are empathetic with the desire to speak again to our dead loved ones. They eagerly look forward to the time of the resurrection when we will live with our loved ones again, as you can see by continuing to read the article cited above. In fact, Jehovah's Witnesses believe that some faithful Christians (spirit-anointed Christians such as ones who lived in the first century and thereafter) have already begun to be resurrected to life in heaven ever since the year 1918, but these resurrected ones do not communicate with or reveal themselves to humans on earth (yet). They are waiting for the time when the full number of 144,000 of them has been fulfilled (Revelation 6:11) and it is time for them to accompany Jesus in waging the war of Armageddon. (Revelation 17:14)