Not one single person past or present, including both Amils and Premils, believes satan is cast into the LOF before the beginning of the millennium. Every single person past or present, including both Amils and Premils, believe satan is cast into the LOF after the millennium.
Amil = the millennium, followed by satan's little season, followed by the 2nd coming = satan is cast into the LOF after the millennium.
Premil = the 2nd coming, followed by the millennium, followed by satan's little season = satan is cast into the LOF after the millennium.
The 2nd coming, followed by satan being cast into the LOF, followed by the millennium = satan is cast into the LOF before the millennium = no view anyone on the planet past or present holds = early Chiliasts are blatantly being misrepresented here.
Hippolytus
Hippolytus of Rome (AD 170-236) states:
“Until the Ancient of days come." That is, when at length the Judge of judges and the King of kings comes from heaven, who shall subvert the whole dominion and power of the adversary, and shall consume all with the eternal fire of punishment. But to His servants, and prophets, and martyrs, and to all who fear Him, He will give an everlasting kingdom; that is, they shall possess the endless enjoyment of good (Fragments on Daniel: Chap. VII.22).
Hippolytus sees the judgment, punishment and destruction of Satan, his minions, the wicked and all evil when Jesus returns. He further explains:
[A]s they wait for the righteous Judge … Then the righteous shall shine forth like the sun, while the wicked shall be shown to be mute and gloomy. For both the righteous and the wicked shall be raised incorruptible: the righteous, to be honoured eternally, and to taste immortal joys; and the wicked, to be punished in judgment eternally … Then shall the son of perdition be brought forward, to wit, the accuser, with his demons and with his servants, by angels stern and inexorable. And they shall be given over to the fire that is never quenched, and to the worm that never sleeps, and to the outer darkness (On the End of the World, Chapter 40).
Modern Bible students might be tempted to impose a common widely-accepted contemporary understanding of “the son of perdition” when reading the writings of Hippolytus, identifying him with a separate entity to the devil, namely the beast or antichrist. But this early Chiliast believed that “the son of perdition” was the devil himself. To reinforce this view, Hippolytus describes “the son of perdition” as “the accuser” – another name Scripture attributes to the evil one (Revelation 12:10). Further, indisputable proof that Hippolytus saw “the son of perdition” as “the devil” can be seen in his teaching in On the End of the World, Chapter 9:
And multitudes of men will run from the east even to the west, and from the north even to the sea, saying, Where is Christ here? Where is Christ there? But being possessed of a vain conceit, and failing to read the Scriptures carefully, and not being of an upright mind, they will seek for a name which they shall be unable to find. For these things must first be; and thus the son of perdition — that is to say, the devil— must be seen (On the End of the World, Chapter 9).
Surely no could deny this explicit explanation.
Now that we have established that Hippolytus believed "the son of perdition" to be "the devil," we should note that he carefully identified his destruction in Chapter 40 (and that of his kingdom) with the second coming. He employs the words of Christ in Matthew 13:41-43 to locate the devil's end. There He teaches: "The Son of man shall send forth his angels, and they shall gather out of his kingdom all things that offend, and them which do iniquity; And shall cast them into a furnace of fire: there shall be wailing and gnashing of teeth. Then shall the righteous shine forth as the sun in the kingdom of their Father."
Like most of His fellow Chiliasts, and like all Amillennialists through the centuries, he saw a general judgment of mankind happening when Christ returns and wickedness finally coming to an end. In Hippolytus mind, this is the time when Satan and his demons "shall be given over to the fire that is never quenched, and to the worm that never sleeps, and to the outer darkness." At the general resurrection/judgment, this arch-enemy of righteousness and the Church is shown to receive his final and eternal judgment. This fits in with the climactic view the early Chiliasts had of the second coming. What awaits the redeemed is a perfected earth free of the bondage of corruption.
He continues:
For the people of the Hebrews shall see Him in human form, as He appeared to them when He came by the holy Virgin in the flesh, and as they crucified Him. And He will show them the prints of the nails in His hands and feet, and His side pierced with the spear, and His head crowned with thorns, and His honourable cross. And once for all shall the people of the Hebrews see all these things, and they shall mourn and weep, as the prophet exclaims, They shall look on Him whom they have pierced; and there shall be none to help them or to pity them, because they repented not, neither turned aside from the wicked way. And these shall go away into everlasting punishment with the demons and the accuser (On the End of the World, 40).
Here once again, the fate of Satan (“the accuser”), “the demons” and the unrepentant is shown to be closely connected. They are all said to face their final doom at the one time. Hippolytus continues in the same book on the same overall narrative:
For at that time the trumpet shall sound, and awake those that sleep from the lowest parts of the earth, righteous and sinners alike. And every kindred, and tongue, and nation, and tribe shall be raised in the twinkling of an eye; and they shall stand upon the face of the earth, waiting for the coming of the righteous and terrible Judge, in fear and trembling unutterable … For both the righteous and the wicked shall be raised incorruptible: the righteous, to be honoured eternally, and to taste immortal joys; and the wicked, to be punished in judgment eternally … the just Judge and the benignant God shall speak to those on the left hand in unmeasured anger and wrath, Depart from me, you cursed, into everlasting fire, prepared for the devil and his angels … Depart from me, you workers of iniquity. I know you not, I recognise you not: you made yourselves the workmen of another lord — namely, the devil. With him inherit the darkness, and the fire that is not quenched, and the worm that sleeps not, and the gnashing of teeth (On the End of the World, 45).
Hippolytus locates the judgment at the return of Christ. He carefully links the punishment of the wicked with the punishment of Satan on Judgment Day. This is a climactic event in Hippolytus’s eyes.