Do you have a Bible reference for "a time when Jesus Christ will rule from Jerusalem on the throne of David over a converted Israel and righteous nations"?
Yes!
Ps 2:6 Yet have I set my king upon my holy hill of Zion.
Ps 10:16 The LORD [is] King for ever and ever: the heathen are perished out of his land.
Ps 24:7 Lift up your heads, O ye gates; and be ye lift up, ye everlasting doors; and the King of glory shall come in.
Ps 24:8 Who [is] this King of glory? The LORD strong and mighty, the LORD mighty in battle.
Ps 24:9 Lift up your heads, O ye gates; even lift [them] up, ye everlasting doors; and the King of glory shall come in.
Ps 24:10 Who is this King of glory? The LORD of hosts, he [is] the King of glory. Selah.
Ps 29:10 The LORD sitteth upon the flood; yea, the LORD sitteth King for ever.
Ps 47:2 For the LORD most high [is] terrible; [he is] a great King over all the earth.
Ps 47:7 For God [is] the King of all the earth: sing ye praises with understanding.
Ps 48:2 Beautiful for situation, the joy of the whole earth, [is] mount Zion, [on] the sides of the north, the city of the great King.
Ps 89:18 For the LORD [is] our defence; and the Holy One of Israel [is] our king.
Ps 95:3 For the LORD [is] a great God, and a great King above all gods.
Ps 98:6 With trumpets and sound of cornet make a joyful noise before the LORD, the King.
Ps 149:2 Let Israel rejoice in him that made him: let the children of Zion be joyful in their King.
Pr 25:5 Take away the wicked [from] before the king, and his throne shall be established in righteousness.
Jer 10:10 But the LORD [is] the true God, he [is] the living God, and an everlasting king: at his wrath the earth shall tremble, and the nations shall not be able to abide his indignation.
Jer 23:5 Behold, the days come, saith the LORD, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth.
Zec 14:9 And the LORD shall be king over all the earth: in that day shall there be one LORD, and his name one.
Mt 5:35 Nor by the earth; for it is his footstool: neither by Jerusalem; for it is the city of the great King.
Isa 11:9 They shall not hurt nor destroy in all my holy mountain: for the earth shall be full of the knowledge of the LORD, as the waters cover the sea.
Isa 45:17 [But] Israel shall be saved in the LORD with an everlasting salvation: ye shall not be ashamed nor confounded world without end.
Jer 23:6 In his days Judah shall be saved, and Israel shall dwell safely: and this [is] his name whereby he shall be called, THE LORD OUR RIGHTEOUSNESS.
Ro 11:26 And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
Jer 23:5 Behold, the days come, saith the LORD, that I will raise unto David a righteous Branch, and a King shall reign and prosper, and shall execute judgment and justice in the earth.
Re 5:10 And hast made us unto our God kings and priests: and we shall reign on the earth.
I began a thread a while back that dealt with "the day of the LORD" where we find out the exact time our Lord returns to put down gentile rule and to claim his rightful place on the Throne of David. Jesus Christ will actually for the first time since he ascended back to heaven in Acts 1 be revealed to every eye on the earth. It truly is the Revelation of Jesus Christ. I will quote some of the event in Re 19.
11 And I saw heaven opened, and behold a white horse; and he that sat upon him [was] called Faithful and True, and in righteousness he doth judge and make war.
12 His eyes [were] as a flame of fire, and on his head [were] many crowns; and he had a name written, that no man knew, but he himself.
13 And he [was] clothed with a vesture dipped in blood: and his name is called The Word of God.
14 And the armies [which were] in heaven followed him upon white horses, clothed in fine linen, white and clean.
15 And out of his mouth goeth a sharp sword, that with it he should smite the nations: and he shall rule them with a rod of iron: and he treadeth the winepress of the fierceness and wrath of Almighty God.
16 And he hath on [his] vesture and on his thigh a name written, KING OF KINGS, AND LORD OF LORDS.
17 And I saw an angel standing in the sun; and he cried with a loud voice, saying to all the fowls that fly in the midst of heaven, Come and gather yourselves together unto the supper of the great God;
18 That ye may eat the flesh of kings, and the flesh of captains, and the flesh of mighty men, and the flesh of horses, and of them that sit on them, and the flesh of all [men, both] free and bond, both small and great.
19 And I saw the beast, and the kings of the earth, and their armies, gathered together to make war against him that sat on the horse, and against his army.
20 And the beast was taken, and with him the false prophet that wrought miracles before him, with which he deceived them that had received the mark of the beast, and them that worshipped his image. These both were cast alive into a lake of fire burning with brimstone.
21 And the remnant were slain with the sword of him that sat upon the horse, which [sword] proceeded out of his mouth: and all the fowls were filled with their flesh.
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.
Alan, please do not laud the KJV if you will not believe what it says.