So John could have made a reference to the 1,000 years in a different way and still have it be grammatically correct? Could you provide an example? (I don't want to put you on the spot, but if you happen to know, I'd appreciate it.)
I am not exactly sure what you are looking for. BUT, in the Revelation 20 in reference to the millennium John refers to the 1000 years BOTH ways - with and without the definite article.
Revelation 20:1 And I saw an angel come down from heaven, having the key of the bottomless pit and a great chain in his hand.
2 And he laid hold on the dragon, that old serpent, which is the Devil, and Satan, and bound him
a thousand years,
3 And cast him into the bottomless pit, and shut him up, and set a seal upon him, that he should deceive the nations no more, till
the thousand years should be fulfilled: and after that he must be loosed a little season.
4 And I saw thrones, and they sat upon them, and judgment was given unto them: and I saw the souls of them that were beheaded for the witness of Jesus, and for the word of God, and which had not worshipped the beast, neither his image, neither had received his mark upon their foreheads, or in their hands; and they lived and reigned with Christ
a thousand years.
5 But the rest of the dead lived not again until
the thousand years were finished. This is the first resurrection.
6 Blessed and holy is he that hath part in the first resurrection: on such the second death hath no power, but they shall be priests of God and of Christ, and shall reign with him
a thousand years.
7 And when
the thousand years are expired, Satan shall be loosed out of his prison,
Look in verse 3 and you will see a non specific use of "a little season" as an example of usage without the definite article.
The fact that John uses the definite article at all with the thousand years proves it is a specific/literal "thousand years".
Verse 6 shows how the definite article is used in koine with "the second death".