According to adherents of 'soul sleep', how did Moses and Elijah appear to Jesus, Peter, James, and John?

As a believer in what people normally call "soul sleep", I don't believe it was a vision, but rather that Elijah and Moses were alive, in heaven, and were simply transported to the Mount of Transfiguration to meet with Jesus.

Elijah, was transported to heaven alive, therefore that isn't a problem. However, Moses definitely did die, so how was it possible for him to be there?

In short, we believe he was resurrected at some point after he died and was taken to heaven. There is some Biblical support for this. For instance, in Jude 1:9, it says:

Yet Michael the archangel, in contending with the devil, when he disputed about the body of Moses, dared not bring against him a reviling accusation, but said, “The Lord rebuke you!”

The reason why this is interesting is because the Archangel Michael makes an appearance here and the Bible makes a connection of the archangel and Jesus Himself at His return in 1 Thessalonians 4:16, (drawing some to believe that the Archangel, arch as in king or commander of angels, is Jesus Himself) and this verse in in connection with the command to resurrect those that sleep in Jesus.

For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and the dead in Christ shall rise first...

Therefore, we believe Moses had been resurrected by God, taken to heaven and was able to appear alive before Jesus at the mount of transfiguration.

The Transfiguration (Matt 17:1-13; cp. Mar 9:2-13) is a vision, an eschatological vision, that Jesus gave the privilege of enjoying to the "inner circle" of his Apostles, Peter, James and John, so that their faith would not abandon them with the apparent total failure on the cross of Jesus Messianic mission, especially as Peter, just "six days earlier", had solemnly proclaimed Jesus as the Messiah (Matt 16:16).

That it was a vision is confirmed by some considerations and details:

• Jesus had already pre-announced this vision, when, after Peter's solemn messianic proclamation and his own immediate reply (so disturbing to the Apostles - and to Peter in particular - with the prediction of the Cross - Matt 16:21) he had promised,

“I tell you the truth, there are some standing here who will not experience death before they see the Son of Man coming in his kingdom.” (Matt 16:28).

In spite of the rather shrouded words, this verse is an allusion to the Transfiguration.

• The figures of Moses and Elijah, together represent perfectly the "Law and Prophets" that Jesus announced he was to fulfill (see Matt 5:17; 7:12; 11:13; 22:40; Luke 16:16; 24:44; John 1:45);
• The vision disappears all of a sudden, as soon as Jesus "touches them" (Matt 17:7-8; cp. Mar 9:8);
• "As they were coming down from the mountain", Jesus explicitly calls it a a vision (Greek: ὅραμα Strong's G3705 - horama) - Matt 17:9), to be kept as a secret for this "inner circle" of his Apostles.

In conclusion: everything is in favour of a vision, and ONLY "metaphysical prejudice", that simple Jewish fishermen from Galilee of the time of Jesus, like Peter, James and John certainly did not share, is in favour of Moses and Elijah as "living disembodied souls", with which Jesus would have conversed in front of the Apostles.

Let the Bible interpret itself.

A few verses later:

And as they came down from the mountain, Jesus charged them, saying, Tell the vision to no man, until the Son of man be risen again from the dead. — Matthew 17:9

Notice that Jesus called the incident a "vision".

The Greek word ὅραμα "horama" is frequently used to indicate a spiritual event, for example it appears 11 times in Acts, such as:

• Acts 9:10 "Said the Lord in a vision"
• 10:17 "Now while Peter doubted in himself what this vision which he had seen should mean"
• 10:19 "While Peter thought on the vision, the Spirit said unto him, Behold, three men seek thee"
• 11:5 "I was in the city of Joppa praying: and in a trance I saw a vision"
• 16:9 "And a vision appeared to Paul in the night"
• 18:9 "Then spake the Lord to Paul in the night by a vision"

It wasn't real. No more than other visions that Peter experienced, such as Peter's vision of the unclean animals:

Now while Peter doubted in himself what this vision which he had seen should mean, … — Acts 10:17

Moses and Elijah weren't really there (how would Peter have known what they look like anyway?), they had long been dead and buried, awaiting the resurrection.

Perhaps this vision was of a conversation between Jesus, Moses, and Elijah that will take place during the Millennium, when the resurrected saints rule and teach along with Jesus in the Kingdom. What Peter saw was a real event, but it didn't happen there and then, two thousand years ago; he was simply privileged enough to be able to experience a vision of an event that still hasn't happened. Like John's own vision of the Millennium, recorded in Revelation, what Peter saw seemed very real at the time.

This also accounts for the comments in the other Gospel stories of this incident where Peter suggests putting them up for the night, not yet realizing how inappropriate that suggestion was:

And it came to pass, as they departed from him, Peter said unto Jesus, Master, it is good for us to be here: and let us make three tabernacles; one for thee, and one for Moses, and one for Elias: not knowing what he said. — Luke 9:33