Why recite the Psalms verses out of order ?
Well, write them in order first, and then notice that, in each case, a small modification helps make more sense of the text; thus,
22:29 For the kingdom is the LORD'S; and He is the ruler over the nations.
24:7-10 Lift up your heads, O ye gates, and be ye lifted up, ye everlasting doors; that the King of glory may come in. 'Who is the King of glory?' 'The LORD strong and mighty, the LORD mighty in battle.' Lift up your heads, O ye gates, yea, lift them up, ye everlasting doors; that the King of glory may come in. 'Who then is the King of glory?' 'The LORD of hosts; He is the King of glory.' Selah
93:1 The LORD reigneth; He is clothed in majesty; the LORD is clothed, He hath girded Himself with strength; yea, the world is established, that it cannot be moved.
Notice how the beginning of 93:1 (“The LORD reigneth”) echoes the same ideas as those reflected in 22:29 (“the kingdom is the LORD'S” and “He is the ruler over the nations”), while, at the same time, the ones immediately following (“He is clothed in majesty” and “He hath girded Himself with strength”) mirror those mentioned in 24:7-10 (“King of glory” and “the LORD strong and mighty, the LORD mighty in battle”). As such, it would make more sense to have 93:1 placed between the other two passages, rather than after them.
106:45 And He remembered for them His covenant, and repented according to the multitude of His mercies.
111:4 He hath made a memorial for His wonderful works; the LORD is gracious and full of compassion. He hath given food unto them that fear Him; He will ever be mindful of His covenant.
It makes more sense to have conjunctions, such as and, which help string up consecutive sentences into a single phrase, placed towards the end of the enumeration, rather than at the beginning; i.e., “X, Y, and Z” instead of “and A, B, C”.
47:6 God is gone up amidst shouting, the LORD amidst the sound of the horn.
81:4 Blow the horn at the new moon, at the full moon for our feast-day.
98:6 With trumpets and sound of the horn shout ye before the King, the LORD.
150:1-6 Hallelujah. Praise God in His sanctuary; praise Him in the firmament of His power. Praise Him for His mighty acts; praise Him according to His abundant greatness. Praise Him with the blast of the horn; praise Him with the psaltery and harp. Praise Him with the timbrel and dance; praise Him with stringed instruments and the pipe. Praise Him with the loud-sounding cymbals; praise Him with the clanging cymbals. Let every thing that hath breath praise the LORD. Hallelujah.
Though not present in the selection itself, the verses immediately succeeding 47:6 make explicit mention of God's kingship, and of His royal throne, whereas both themes are completely absent from Psalm 81 in its entirety; as such, it would make more sense to move 98:6 closer to 47:6, since both passages exhibit similar patterns of thought and expression.