How do proponents of Apokatastasis deal with the "Everlasting punishment" texts in scripture?

Those who believe in Apokatastasis believe Revelation 20:10 is grossly misunderstood. The Greek says:

καὶ ὁ διάβολος ὁ πλανῶν αὐτοὺς ἐβλήθη εἰς τὴν λίμνην τοῦ πυρὸς καὶ θείου, ὅπου καὶ τὸ θηρίον καὶ ὁ ψευδοπροφήτης, καὶ βασανισθήσονται ἡμέρας καὶ νυκτὸς εἰς τοὺς αἰῶνας τῶν αἰώνων.

And the devil that deceived them was cast into the lake of fire and brimstone, where the beast and the false prophet are, and shall be tormented day and night for ever and ever- KJV

The Lake of Fire

The first thing that's significant is the Lake of Fire. A lake is a body of water. Water extinguishes fire, so this doesn't make sense. Therefore, we would interpret this metaphorically. Water cleanses and fire purifies. Yeshua says:

"For every one shall be salted with fire, and every sacrifice shall be salted with salt." Mark 9:49

Other examples include:

"That the trial of your faith, being much more precious than of gold that perisheth, though it be tried with fire, might be found unto praise and honour and glory at the appearing of Jesus Christ" 1 Peter 1:7

"Behold, I have refined thee, but not with silver; I have chosen thee in the furnace of affliction." Isaiah 48:10

"But who may abide the day of his coming? and who shall stand when he appeareth? for he is like a refiner's fire, and like fullers' soap: And he shall sit as a refiner and purifier of silver: and he shall purify the sons of Levi, and purge them as gold and silver, that they may offer unto YHVH an offering in righteousness." Malachi 3:2

"And the sight of the glory of YHVH was like devouring fire on the top of the mount in the eyes of the children of Israel." Exodus 24:17

"For our God is a consuming fire." Hebrews 12:49

θείου

θείου means "brimstone". According to Thayer's Greek Lexicon:

θεῖον, θείου, τό (apparently the neuter of the adjective θεῖος equivalent to divine incense, because burning brimstone was regarded as having power to purify, and to ward off contagion (but Curtius, § 320 allies it with θύω; cf. Latinfumus, English dust)), brimstone: Luke 17:29; Revelation 9:17; Revelation 14:10; Revelation 19:20; (); . (Genesis 19:24; Psalm 10:6 (); Ezekiel 38:22; Homer, Iliad 16, 228; Odyssey 22, 481, 493; (Plato) Tim. Locr., p. 99 c.; Aelian v. h. 13, 15 (16); Herodian, 8, 4, 26 (9 edition, Bekker).)

So brimstone was believed to have the power to purify.

βασανίζω

The next word is βασανίζω. Thayer's Greek Lexicon says the very first definition is:

1. properly, to test (metals) by the touchstone.

βασανίζω means to test, examine, or to cause distress. The only sort of "torment" associated with this word in the NT is mental torment, and it definitely does not mean "torture". Here are some more examples of this word, and hopefully this will paint a clearer picture of what it means:

But the ship was now in the midst of the sea, tossed (βασανιζόμενον) with waves: for the wind was contrary. Matthew 14:24

How is it that a ship was "tortured"? However, if the waves were testing the strength and endurance of the ship, causing it distress, it is understandable why Matthew would use βασανιζόμενον here. Robert Young (Young's Literal Transaltion) understood this, and translates:

and the boat was now in the midst of the sea, distressed by the waves, for the wind was contrary.

Mark uses this same word to describe this same event, but uses it a bit differently:

"And he saw them toiling (βασανιζομένους) in rowing; for the wind was contrary unto them: and about the fourth watch of the night he cometh unto them, walking upon the sea, and would have passed by them." Mark 6:48

Instead of the boat, it is the disciples who are having βασανίζω acted upon then. The American Standard Version says:

And seeing them distressed in rowing, for the wind was contrary unto them, about the fourth watch of the night he cometh unto them, walking on the sea; and he would have passed by them

αἰών

The last word is αἰών and it is probably the most debated word in the bible. This word means "age". It always means age, and there is no reason to translate it any other way. For example:

"And the cares of this world (αἰών), and the deceitfulness of riches, and the lusts of other things entering in, choke the word, and it becometh unfruitful." Mark 4:19

The KJV chose the word "world", which is a bit deceitful because Greek already has a word for world...κόσμος. If we say "the cares of this forever choke the word", that doesn't make a lot of sense. Here is every instance of αἰών in the NT. Replace each word with "age" and it makes perfect sense everytime. Actually, the interlinear does it for you, because it's a literal translation and they know αἰών means age.

Conclusion

Those who believe in Apokatastasis would interpret Revelation 20:10 to be:

"and the devil, the [one] deceiving them, was cast into the lake of the fire and of brimstone (to be purified), where also the beast and the false prophet [are], and they will be examined/tested night and day for the ages of the ages"- very literal translation