No. The Revelation 20 millennium is the present Gospel age, where our covenant relationship with Christ is established,
Your "obvious problems with a millennial fulfilment" are that the Millennium is specified as a 1,000 year period,
not some "approximately 2,000 year period", or "some indefinite period of time in excess of 1,900 years".
"Palestinian Covenant" to Israel (pure genetic Hebrews):
1 And it shall come to pass, when all these things are come upon thee, the blessing and the curse, which I have set before thee, and thou shalt call them to mind among all the nations, whither the Lord thy God hath driven thee,
2 And shalt return unto the Lord thy God, and shalt obey his voice according to all that I command thee this day, thou and thy children, with all thine heart, and with all thy soul;
3 That then the Lord thy God will turn thy captivity, and have compassion upon thee, and will return and gather thee from all the nations, whither the Lord thy God hath scattered thee.
4 If any of thine be driven out unto the outmost parts of heaven, from thence will the Lord thy God gather thee, and from thence will he fetch thee:
5 And the Lord thy God will bring thee into the land which thy fathers possessed, and thou shalt possess it; and he will do thee good, and multiply thee above thy fathers.
6 And the Lord thy God will circumcise thine heart, and the heart of thy seed, to love the Lord thy God with all thine heart, and with all thy soul, that thou mayest live.
7 Therefore, behold, the days come, saith the Lord, that they shall no more say, The Lord liveth, which brought up the children of Israel out of the land of Egypt;
8 But, The Lord liveth, which brought up and which led the seed of the house of Israel out of the north country, and from all countries whither I had driven them; and they shall dwell in their own land.
21 And say unto them, Thus saith the Lord God; Behold, I will take the children of Israel from among the heathen [Gentiles], whither they be gone, and will gather them on every side, and bring them into their own land:
22 And I will make them one nation in the land upon the mountains of Israel; and one king shall be king to them all: and they shall be no more two nations, neither shall they be divided into two kingdoms any more at all.
23 Neither shall they defile themselves any more with their idols, nor with their detestable things, nor with any of their transgressions: but I will save them out of all their dwellingplaces, wherein they have sinned, and will cleanse them: so shall they be my people, and I will be their God.
24 And David my servant shall be king over them; and they all shall have one shepherd: they shall also walk in my judgments, and observe my statutes, and do them.
25 And they shall dwell in the land that I have given unto Jacob my servant, wherein your fathers have dwelt; and they shall dwell therein, even they, and their children, and their children's children for ever: and my servant David shall be their prince for ever.
The 1,000 year Millennium is the final dispensation before entering eternity. It is a dispensation where mortal man - even under
the very best of (Edenic) circumstances - still fails to overcome his a sin-nature, thus proving that man needs a Savior from sin.
Yet have I set my king upon my holy hill of Zion.
I will declare the decree: the LORD hath said unto me,
Thou art my Son; this day have I begotten thee.
Ask of me, and I shall give thee the heathen for thine inheritance,
and the uttermost parts of the earth for thy possession.