Why would you think this period should ever end, if His reign was everlasting?
That is one reason you claim premil limit His eternal reign. His Second Coming has nothing to do with an interruption to, nor a start of any reign. Premil do not claim His reign starts at the Second Coming. Premil claim the Second Coming brings Christ physically to earth to continue His eternal reign on earth. In the NHNE that reign continues in the New Jerusalem. To even state the reign ends at the Second Coming is hypocritical to the point. Premil does not limit this reign any more than Amil does. This point should be debunked, as ridiculous.
If you claim this misrepresents amil, then certainly amil misrepresent premil in the same fashion. The Word has always been in a position of authority. Nothing that happens on earth will ever change that authority. The disciples had power and authority years before the death, burial, and resurrection of Christ.
The thousand years as presented cannot nor ever will represent an intra-Advent period. Christ rules and reigns on earth period, no exceptions, during the Millennium. Since Christ is on earth, and amil cannot prove Christ is not on earth, then the Millennium takes place after the Second Coming. Recap is just an imagination of a biased position in an erroneous eschatology. Where is proof that an ascension is implied in Revelation 20? The context is the tribulation and especially the end of Satan's 42 months with the FP and the beast. The context is the end and defeat of Satan, the FP, and the beast. That context does not end until this verse:
"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."
No context about the first century AD can be found nor implied. That is only human opinion and imagination.